## NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes

In NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary we learn about different shaps. Ncert Solutions are provided by our expert teachers. In NCERT Solutions Class 6 Maths Chapter 5 there are 9 exerrcise.

we will discuss corners, edges, planes, open curves and closed curves in our surroundings. We organise them into line segments, angles, triangles, polygons and circles.

### NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercises 5.1

Class 6th Maths Chapter 5 Solutions ex 5.1

**Q.1. What is the disadvantage in comparing line segments by mere observation?**

Ans:-

Comparing the lengths of two line segments simply by ‘observation’ may not be accurate. So we use a divider to compare the length of the given line segments.

**Q.2. Why is it better to use a divider than a ruler, while measuring the length of a line segment?**

Ans:-

While using a ruler, chances of error occur due to the thickness of the ruler and angular viewing. Hence, using divider accurate measurement is possible.

**Q.3 Draw any line segment, say AB¯¯¯¯¯¯¯¯. Take any point C lying in between A and B. Measure the lengths of AB, BC, and AC. Is AB = AC + CB?****[Note: If A, B, C are any three points on a line such AC + CB = AB, then we can be sure that C lies between A and B]**

Ans:-

A, B and C such that C lies between A and B and AB = 7 cm.

AC = 3 cm, CB = 4 cm.

∴ AC + CB = 3 cm + 4 cm = 7 cm.

But, AB = 7 cm.

So, AB = AC + CB.

**Q.4. If A, B, C are three points on a line such that AB = 5 cm, BC = 3 cm, and AC = 8 cm, which one of them lies between the other two?**

Ans:-

AB = 5 cm

BC = 3 cm

AB + BC = 5 + 3 = 8 cm

But, AC = 8 cm

Hence, B lies between A and C.

**5. Verify, whether D is the midpoint of** AG¯¯¯¯¯¯¯¯.

Ans:-

From the given figure, we have

AG = 7 cm – 1 cm = 6 cm

AD = 4 cm – 1 cm = 3 cm

and DG = 7 cm – 4 cm = 3 cm

∴ AG = AD + DG.

Hence, D is the midpoint of AG¯¯¯¯¯¯¯¯.

**Q.6. If B is the midpoint** of AC¯¯¯¯¯¯¯¯ and C is the midpoint** of BD¯¯¯¯¯¯¯¯, where A, B, C, D lie on a straight lin**e**, say why AB = CD?**

Ans:-

given B is the midpoint of AC.

∴ AB = BC …(i)

C is the mid-point of BD.

BC = CD…(ii)

From Eq.(i) and (ii), We have

AB = CD

**Q.7. Draw five triangles and measure their sides. Check-in each case, if the sum of the lengths of any two sides is always less than the third side.**

Ans:-**Case 1. In triangle ABC**

Let AB = 2.5 cm

BC = 4.8 cm

and AC = 5.2 cm

AB + BC = 2.5 cm + 4.8 cm

= 7.3 cm

Since, 7.3 > 5.2

So, AB + BC > AC

Hence, sum of any two sides of a triangle is greater than the third side.

**Case 2. In triangle PQR**

Let PQ = 2 cm

QR = 2.5 cm

and PR = 3.5 cm

PQ + QR = 2 cm + 2.5 cm = 4.5 cm

Since, 4.5 > 3.5

So, PQ + QR > PR

Hence, sum of any two sides of a triangle is greater than the third side.

**Case 3. In triangle XYZ**

Let XY = 5 cm

YZ = 3 cm

and ZX = 6.8 cm

XY + YZ = 5 cm + 3 cm

= 8 cm

Since, 8 > 6.8

So, XY + YZ > ZX

Hence, the sum of any two sides of a triangle is greater than the third side.

**Case 4. In triangle MNS**

Let MN = 2.7 cm

NS = 4 cm

MS = 4.7 cm

and MN + NS = 2.7 cm + 4 cm = 6.7 cm

Since, 6.7 >4.7

So, MN + NS > MS

Hence, the sum of any two sides of a triangle is greater than the third side

**Case 5. In triangle KLM**

Let KL = 3.5 cm

LM = 3.5 cm

KM = 3.5 cm

and KL + LM = 3.5 cm + 3.5 cm = 7 cm

7 cm > 3.5 cm

Solution:

(i) For one-fourth revolution, we have

So, KL + LM > KM

Hence, the sum of any two sides of a triangle is greater than the third side.

Hence, we conclude that the sum of any two sides of a triangle is never less than the third side.

### NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercises 5.2

Ch 5 Class 6 Maths Solutions ex 5.2

**Q.1. What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from****(a) 3 to 9**

Ans:-

9 – 3 = 6 ÷ 12 = 1/2 of a revolution**(b) 4 to 7**

Ans:-

7 – 4 = 3 ÷ 12 = 1/4 of a revolution**(c) 7 to 10**

Ans:-

10 – 7 = 3 ÷ 12 = 1/4 of a revolution**(d) 12 to 9**

Ans:-

9 – 0 = 9 ÷ 12 = 3/4 of a revolution**(e) 1 to 10**

Ans:-

10 – 1 = 9 ÷ 12 = 3/4 of a revolution**(f) 6 to 3**

Ans:-

6 to 3 i.e., 6 to 12 and then 12 to 3

6 to 12 = 12 – 6 = 6 and 12 to 3 = 0 to 3 = 3 – 0 = 3

6 + 3 = 9 ÷ 12 = 3/4 of a revolution

**Q.2. Where will the hand of a clock stop if it****(a) starts at 12 and makes 1 / 2 of a revolution, clockwise?**

Ans:-

Starting from 12 and making 1/2 of a revolution, the clock hand stops at 6.

**(b) starts at 2 and makes 1 / 2 of a revolution, clockwise?**

Ans:-

Starting from 2 and making 1/2 of a revolution, the clock hand stops at 8.

**(c) starts at 5 and makes 1 / 4 of a revolution, clockwise?**

Ans:-

Starting from 5 and making 1/2 of a revolution, the clock hand stops at 8.

**(d) starts at 5 and makes 3 / 4 of a revolution, clockwise?**

Ans:-

Starting from 5 and making 1/2 of a revolution, the clock hand stops at 2

**Q.3. Which direction will you face if you start facing(a) east and make 1 / 2 of a revolution clockwise?(b) east and make 1 ½ of a revolution clockwise?(c) west and make 3 / 4 of a revolution anti-clockwise?(d) south and make one full revolution?(should we specify clockwise or anti-clockwise for this last question? Why not?)**

Taking one full revolution we will reach back to the original (starting) position. Therefore, it makes no difference whether we turn clockwise or anticlockwise.

**Q.4. What part of a revolution have you turned through if you stand facing****(a) east and turn clockwise to face north?**

Ans:-

If we start from east and reach north (turning clockwise) 3/4 of a revolution is required

**(b) south and turn clockwise to face east**

Ans:-

If we start from south turning clockwise to face east, 3/4 of a revolution is required.

**(c) west and turn clockwise to face east?**

Ans:-

If we start from west turning clockwise to face east, 1/2 of a revolution is required.

**5. Find the number of right angles turned through by the hour hand of a clock when it goes from****(a) 3 to 6**

Ans:-

Starting from 3 to 6, the hour hand turns through 1 right angle.

**(b) 2 to 8**

Ans:-

Starting from 2 to 8, the hour hand turns through 2 right angles.

**(c) 5 to 11**

Ans:-

Starting from 5 to 11, the hour hand turns through 2 right angles

**(d) 10 to 1**

Ans:-

Starting from 10 to 1, the hour hand turns through 1 right angle

**(e) 12 to 9**

Ans:-

Starting from 12 to 9, the hour hand turns through 3 right angles.

**(f) 12 to 6**

Ans:-

Starting from 12 to 6, the hour hand turns through 2 right angles.

**Q.6. How many right angles do you make if you start facing**

(a) south and turn clockwise to the** **west?

(b) north and turn anti-clockwise to the east?

(c) west and turn to west?

(d) south and turn to the north?

Ans:-

**Q.7. Where will the hour hand of a clock stop if it starts****(a) from 6 and turns through 1 right angle?**

Ans:-

Starting from 6 and turning through 1 right angle, the hour hand stops at 9

**(b) from 8 and turns through 2 right angles?**

Ans:-

Starting from 8 and turning through 2 right angles, the hour hand stops at 2.

**(c) from 10 and turns through 3 right angles?**

Ans:-

Starting from 10 and turning through 3 right angles, the hour hand stops at 7.

**(d) from 7 and turns through 2 straight angles?**

Ans:-

Starting from 7 and turning through 2 right angles, the hour hand stops at 7

### NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercises 5.3

Class 6th Maths Chapter 5 Solution ex 5.3

**Q.1 Match the following:(i) Straight angle (a) Less than one-fourth of a revolution.(ii) Right angle (b) More than half a revolution.(iii) Acute angle (c) Half of a revolution.(iv) Obtuse angle (d) One-fourth of a revolution.(v) Reflex angle (e) Between 1/4 and 1/2 of a revolution.– (f) One complete revolution**

Ans:-

(i) Straight angle ↔ (c) Half of a revolution.

(ii) Right angle ↔ (d) One-fourth of a revolution.

(iii) Acute angle ↔ (a) Less than one-fourth of a revolution.

(iv) Obtuse angle ↔ (e) Between 1/4 and 1/2 of a revolution.

(v) Reflex angle ↔ (f) One complete revolution, right, acute, obtuse or reflex

**Q.2. Classify each one of the following angles as right, straight, acute, obtuse, or reflex:**

Ans:-

(a) Acute angle

(b) Obtuse angle

(c) Right angle

(d) Reflex angle

(e) Straight angle

(f) Acute angle

### NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercises 5.4

Ch 5 Class 6 Maths Solutions ex 5.4

**Q.1. What is the measure of****(i) a right angle?**

Ans:-

Measure of a right angle = 90°**(ii) a straight angle**

Ans:-

Measure of a straight angle = 180°

**Q.2. Say True or False:****(a) The measure of an acute angle < 90 ^{0}**

**(b) The measure of an obtuse angle < 90**

^{0}**(c) The measure of a reflex angle > 180**

^{0}**(d) The measure of one complete revolution = 360**

^{0}**(e) If m ∠A = 53**

^{0}and m ∠B = 35^{0}, then m ∠A > m ∠B.Ans:-

(a) True

(b) False

(c) True

(d) True

(e) True

**Q.3. Write down the measures of****(a) some acute angles**

Ans:-

20°, 55°, and 70° are acute angles.**(b) some obtuse angles**

Ans:-

110°, 150°, and 175° are obtuse angles.

**Q.4. Measures the angles given below using the protractor and write down the measure.**

(i) 45°

(ii) 125°

(iii) 90°

(iv) ∠1 = 60°, ∠2 = 90°, ∠3 = 125°

**Q.5. Which angle has a large measure? First, estimate and then measure.****Measure of Angle A =****Measure of Angle B =**

Ans:-

Measure of Angle A = 40°

Measure of Angle B = 60°.

**Q.6. From these two angles which has larger measure? Estimate and then confirm by measuring them.**

Ans:-

Measure of angle (a) = 45°

and the measure of angle (b) = 60°

**Q.7. Fill in the blanks with acute, obtuse, right or straight:****(a) An angle whose measure is less than that of a right angle is _____**

Ans:- acute**(b) An angle whose measure is greater than that of a right angle is ____**

Ans:- obtuse**(c) An angle whose measure is the sum of the measures of two right angles is _______**

Ans:- straight**(d) When the sum of the measures of two angles is that of a right angle, then each one of them is _____**

Ans:- acute**(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be ______**

Ans:- obtuse

**8. Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).**

(a) Measure of the angle = 40°

(b) Measure of the angle = 130°

(c) Measure of the angle = 65°

(d) Measure of the angle = 135°.

**Q.9. Find the angle measure between the hands of the clock in each figure:**

Ans:-

(i) The angle between the hour hand and minute hand of a clock at 9.00 a.m = 90°

(ii) The angle between the hour hand and minute hand of a clock at 1.00 p.m = 30°

(iii) The angle between the hour hand and minute hand of a clock at 6.00 p.m = 180°.

**10. InvestigateIn the given figure, the angle measure 30°. Look at the same figure through a magnifying glass. Does the angle become larger? Does the size of the angle change?**

Ans:-

It is an activity. So try it yourself.

**11. Measure and classify each angle:**

Angle | Measure | Type |

<AOB | ||

<AOC | ||

<BOC | ||

<DOC | ||

<DOA | ||

<DOB |

Ans:-

Angle | Measure | Type |

<AOB | 40^{0} | Acute |

<AOC | 125^{0} | Obtuse |

<BOC | 85^{0} | Acute |

<DOC | 95^{0} | Obtuse |

<DOA | 140^{0} | Obtuse |

<DOB | 180^{0} | Straight |

### NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercises 5.5

NCERT solutions for class 6 maths chapter 5 ex 5.5

**Q.1. Which of the following are models for perpendicular lines:****(a) The adjacent edges of a table top.**

Ans:-

Yes, the adjacent edges of a table top are the models of perpendicular lines.**(b) The lines of a railway track.**

Ans:-

No, The lines of a railway track are parallel to each other. So they are not a model for perpendicular lines.**(c) The line segments forming the letter ‘L’.**

Ans:-

Yes, the two-line segments of‘L’ are the model of perpendicular lines.**(d) The letter V.**

Ans:-

No, the two line segments of ‘V’ are not a model for perpendicular lines.

**Q.2 Let PQ¯¯ be the perpendicular to the line segment XY¯¯ Let PQ¯¯ and XY¯¯ intersect at in the point A. What is the measure of ∠PAY?**

Ans:-

Since PQ¯¯ ⊥ XY

∴ ∠PAY = 90°

**3. There are two set squares in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common?**

Ans:-

The measure of angles in one set square are 30^{0}, 60^{0} and 90^{0}

The other set square has a measure of angles 45^{0}, 45^{0} and 90^{0}

Yes, the angle of measure 90^{0} is common in between them

**4. Study the diagram. The line l is perpendicular to line m****(a) Is CE = EG?**

**(b) Does PE bisect CG?****(c) Identify any two line segments for which PE is the perpendicular bisector.****(d) Are these true?****(i) AC > FG****(ii) CD = GH****(iii) BC < EH.**

Ans:-

(a) Yes, since, CE = 2 units and EG = 2 units respectively

(b) Yes. Since, CE = EG as both are of 2 units. Hence PE bisect CG

(c) and are the line segments for which PE is the perpendicular bisector

(d) (i) True. Since AC = 2 units and FG = 1 unit

∴ AC > FG

(ii) True because both are of 1 unit

(iii) True. Since, BC = 1 unit and EH = 3 units

∴ BC < EH

### NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercises 5.6

class 6 maths chapter 5 solutions ex 5.6

**1. Name the types of following triangles:****(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.**

Ans:-

All sides of the given triangle are different

Hence, it is a Scalene triangle.**(b) ∆ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.**

Ans:-

All sides of the given triangle are different

Hence, it is a Scalene triangle.**(c) ∆PQR such that PQ = QR = PR = 5 cm.**

Ans:-

All sides are equal.

Hence, it is an equilateral triangle.**(d) ∆DEF with ∠D = 90°**

Ans:-

Given that: In ∆DEF, m∠D = 90°

Hence it is a right-angled triangle**(e) ∆XYZ with ∠Y = 90° and XY = YZ.**

Ans:-

Given that: In ∆XYZ, m∠Y = 90° and XY = YZ

Hence it is a right-angled triangle**(f) ∆LMN with ∠L = 30°, ∠M = 70° and ∠N = 80°**

Ans:-

Given that: ∆LMN, m∠L = 30°, m ∠M = 70° and m∠N = 80°.

Hence it is an acute-angled triangle.

**Q.2. Match the following:Measures of Triangle Type of Triangle(i) 3 sides of equal length (a) Scalene(ii) 2 sides of equal length (b) Isosceles right-angled(iii) All sides are of different length (c) Obtuse angled(iv) 3 acute angles (d) Right-angled(v) 1 right angle (e) Equilateral(vi) 1 obtuse angle (f) Acute angled(vii) 1 right angle with two sides of equal length (g) Isosceles**

Ans:-

(i) ↔ (e)

(ii) ↔ (g)

(iii) ↔ (a)

(iv) ↔ (f)

(v) ↔ (d)

(vi) ↔ (c)

(vii) ↔ (b)

**Q.3. Name each of the following triangles in two different ways: (you may judge the nature of the angle by observation)**

**(a)** (i) Acute angled triangle

(ii) Isosceles triangle**(b)** (i) Right-angled triangle

(ii) Scalene triangle**(c)** (i) Obtuse angled triangle

(ii) Isosceles triangle**(d)** (i) Right-angled triangle

(ii) Isosceles triangle**(e)** (i) Acute angled triangle

(ii) Equilateral triangle**(f)** (i) Obtuse angled triangle

(ii) Scalene triangle.

**Q.4. Try to construct triangles using match sticks. Some are shown here. Can you make a triangle with****(a) 3 matchsticks?****(b) 4 matchsticks?****(c) 5 matchsticks?****(d) 6 matchsticks?****(Remember you have to use all the available matchsticks in each case)****Name the type of triangle in each case. If you cannot make a triangle, think of reasons for it**

Ans:-

(a) Yes, we can make an equilateral triangle with 3 matchsticks

(b) No, we cannot make a triangle with 4 matchsticks

(c) Yes, we can make an equilateral triangle with 5 matchsticks

(d) Yes, we can make an equilateral triangle with 6 matchsticks

### NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercises 5.7

Ch 5 class 6 maths solutions ex 5.7

**Q.1. Say True or False:****(a) Each angle of a rectangle is a right angle.**

Ans:-True,**(b) The opposite sides of a rectangle are equal in length.**

Ans:-True,**(c) The diagonals of a square are perpendicular to one another.**

Ans:-True,**(d) All the sides of a rhombus are of equal length.**

Ans:- True,**(e) All the sides of a parallelogram are of equal length.**

Ans:-False,**(f) The opposite sides of a trapezium are parallel.**

Ans:-False,

**Q.2. Give reasons for the following:****(a) A square can be thought of as a special rectangle.**

Ans:-

A square has all the properties of a rectangle.

So, it is a special rectangle.**(b) A rectangle can be thought of as a special parallelogram.**

Ans:-

A rectangle has the same properties as that of a parallelogram.

So, it is a special parallelogram

**(c) A square can be thought of as a special rhombus.**

Ans:-

A square has the same properties as that of a rhombus.

So, it is a special rhombus.**(d) Squares, rectangles, parallelograms are all quadrilaterals.**

Ans:-

Square, rectangles, and parallelogram are all quadrilateral as they are all enclosed by four sides**(e) Square is also a parallelogram.**

Ans:-

All 4 sides are of same length. Therefore a square is a special parallelogram.

**Q.3. A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?**

Ans:-

Square is only the regular quadrilateral with equal sides and equal angles.

Therefore, the square is a regular quadrilateral.

### NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercises 5.8

class 6th maths chapter 5 solutions ex 5.8

**Q.1. Examine whether the following are polygons. If anyone among them is not, say why?**

(a) It is not a closed figure. Hence, it is not a polygon.

(b) It is a polygon made of six sides

(c) No it is not a polygon because it is not made of line segments.

(d) It is not a polygon as it is not made of line segments.

**Q.2. Name each polygon.**

(a) A quadrilateral:- A shape has four sides is know as Quadrilateral.

More Examples:-

(b) A Triangle :- A shape has three sides is know as Triangle.

More Examples:-

(c) A Pentagon :- A shape has five sides is know as Pentagon.

More Examples:-

(d) A Octagon :- A shape has 8 sides is know as Octagon.

More Examples:-

**Q.3. Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of triangle you have drawn.**

Ans:-

abcdef is a rough sketch of a regular hexagon. If we join any three vertices like a, b, and c, we get a scalene triangle abc.

**Q.4. Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.**

Ans:-

PQRSTUVW is a rough sketch of a regular octagon. PQTU is the rectangle formed by joining the four vertices of the given octagon.

**Q.5. A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.**

Ans:-

From the figure we may find ac, ad, bd, be and ce are the diagonals

### NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercises 5.9

NCERT Class 6 Maths Chapter 5 Solutions ex 5.9

**Match the following :**

Ans:-

(a) 4 ↔ (ii)

Examples:- An ice-cream cone And Birthday cap

(b) ↔ (iv)

Examples:- Tennis ball And Cricket ball

(c) ↔ (v)

Examples:- A road roller And A lawn roller

(d) ↔ (iii)

Examples:- Math book And A brick

(e) ↔ (i)

Examples:- A diamond And Egypt-Pyramids

**Q.2. What shape is****(a) Your instrument box?**

Ans:-

The shape of instrument box is cuboid.**(b) A brick?**

Ans:-

The shape of a brick is cuboid.**(c) A match box?**

Ans:-

The shape of a matchbox is cuboid.**(d) A road-roller?**

Ans:-

The shape of a road-roller is a cylinder.**(e) A sweet laddu?**

Ans:-

The shape of a sweet laddu is a sphere.

Class 6 Science NCERT Notes | Class 6 Complete Study Material |

NCERT Solutions for Class 6 Science | Class 6 Maths Chapter 6 Solutions |

NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes are based on NCERT Books. You can download ncert book for class 6 maths chapter 5.

## What we learn ?

- The distance between the end points of a line segment is its length.
- A graduated ruler and the divider are useful to compare lengths of line

segments. - When a hand of a clock moves from one position to another position we have

an example for an angle. One full turn of the hand is 1 revolution. A right angle is ¼ revolution and a straight angle is ½ a revolution . We use a protractor to measure the size of an angle in degrees. The measure of a right angle is 90° and hence that of a straight angle is 180°.

An angle is acute if its measure is smaller than that of a right angle and is obtuse if its measure is greater than that of a right angle and less than a straight angle. A reflex angle is larger than a straight angle.Two intersecting lines are perpendicular if the angle between them is 90°. - The perpendicular bisector of a line segment is a perpendicular to the line
- segment that divides it into two equal parts.
- Triangles can be classified as follows based on their angles:

Nature of angles in the triangle | Name |

Each angle is acute One angle is a right angle One angle is obtuse | Acute angled triangle Right angled triangle Obtuse angled triangle |

7. Triangles can be classified as follows based on the lengths of their sides:

Nature of sides in the triangle | Name |

All the three sides are of unequal length Any two of the sides are of equal length All the three sides are of equal length | Scalene triangle Isosceles triangle Equilateral triangle |

8. Polygons are named based on their sides.

Number of sides | Name of the Polygon |

3 4 5 6 8 | Triangle Quadrilateral Pentagon Hexagon Octagon |

9. Quadrilaterals are further classified with reference to their properties.

Properties | Name of the Quadrilateral |

One pair of parallel sides Two pairs of parallel sides Parallelogram with 4 right angles Parallelogram with 4 sides of equal length A rhombus with 4 right angles | Trapezium Parallelogram Rectangle Rhombus Square |

- We see around us many three dimensional shapes. Cubes, cuboids, spheres,

cylinders, cones, prisms and pyramids are some of them.