EduSahara™ Worksheet

Question 1

1.

Which of the following are true?

a)	Any two triangles are congruent.
b)	Any two circles are similar.
c)	Any two squares are congruent.
d)	Any two circles are congruent.
e)	Any two triangles are similar.
f)	Any two squares are similar.

(i)

{d,e,b}
(ii)

{a,b}
(iii)

{b,f}
(iv)

{c,f}
(v)

{a,f,b}

Question 2

2.

Which of the following are true?

a)	A triangle is a polygonal region.
b)	A sector is a polygonal region.
c)	A square is a polygonal region.
d)	A circle is a polygonal region.
e)	A semi-circle is a polygonal region.

(i)

{d,c,a}
(ii)

{b,a}
(iii)

{d,c}
(iv)

{e,b,a}
(v)

{a,c}

Question 3

3.

Which of the following are true?

a)	Congruent figures have same area.
b)	If two figures are congruent, then they are similar too.
c)	Similar and congruent are not synonymous.
d)	If two figures are similar, then they are congruent too.
e)	Similar figures have same area.

(i)

{d,e,c}
(ii)

{d,a}
(iii)

{a,b,c}
(iv)

{d,a,b}
(v)

{e,b}

Question 4

4.

Which of the following are true?

a)	Area of the union of two polygonal region is the sum of the individual area.
b)	Area of the union of two polygonal region is not equal to the sum of the individual area.
c)	A polygonal region can be divided into a finite number of triangles in a unique way.
d)	Area of a convex polygonal region is equal to the sum of the areas of all triangles formed by joining the vertices of the polygon with an interior point.

(i)

{a,b}
(ii)

{a,c,b}
(iii)

{a,d,b}
(iv)

{c,d}
(v)

{b,d}

Question 5

5.

Which of the following are necessary conditions for similarity of two polygons ?

a)	The corresponding angles are proportional.
b)	The corresponding sides are proportional.
c)	The corresponding angles are equal.
d)	The corresponding sides are equal.

(i)

{b,c}
(ii)

{a,d,b}
(iii)

{a,c,b}
(iv)

{d,c}
(v)

{a,b}

Question 6

6.

Which of the following are true?

a)	Similarity is transitive.
b)	Similarity is reflexive.
c)	Similarity is anti symmetric.
d)	Similarity is symmetric.

(i)

{c,d}
(ii)

{c,a,b}
(iii)

{c,b}
(iv)

{c,a}
(v)

{a,b,d}

Question 7

7.

Which of the following are true?

a)	Any two quadrilaterals are similar if the corresponding sides are proportional.
b)	Any two quadrilaterals are similar if the corresponding angles are equal.
c)	Any two triangles are similar if the corresponding sides are proportional.
d)	Any two triangles are similar if the corresponding angles are equal.

(i)

{b,c}
(ii)

{b,a}
(iii)

{b,a,c}
(iv)

{b,d}
(v)

{a,c,d}

Question 8

8.

The ratio of the bases of two triangles ABC and DEF is
10

:

4
.

If the triangles are equal in area, then the ratio of their heights is

(i)

11

:

4
(ii)

10

:

6
(iii)

4

:

10
(iv)

10

:

1
(v)

9

:

4

Question 9

9.

△ABC is a triangle with sides BC = 13 cm, CA = 12 cm and AB = 14 cm. △ABC is reduced to △A'B'C' such that the smallest side of △A'B'C' is 5.33 cm. Find the scale factor.

(i)

4
9
(ii)

4
11
(iii)

4
7
(iv)

2
3
(v)

2
9

Question 10

10.

△ABC is a triangle with sides BC = 14 cm, CA = 10 cm and AB = 11 cm. △ABC is enlarged to △A'B'C' such that the smallest side of △A'B'C' is 30 cm. Find the corresponding lengths of the enlarged triangle △A'B'C'.

(i)

42 cm, 30 cm, 33 cm
(ii)

44 cm, 32 cm, 35 cm
(iii)

43 cm, 31 cm, 34 cm
(iv)

41 cm, 29 cm, 32 cm
(v)

40 cm, 28 cm, 31 cm

Question 11

11.

AB = 18.00 cm, BC = 9.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 24000. Calculate the diagonal distance of the field.

(i)

2.83 km
(ii)

3.83 km
(iii)

5.83 km
(iv)

6.83 km
(v)

4.83 km

Question 12

12.

AB = 19.00 cm, BC = 16.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 15000. Calculate the area of the field.

(i)

7.84 sq.km
(ii)

4.84 sq.km
(iii)

6.84 sq.km
(iv)

5.84 sq.km
(v)

8.84 sq.km

Question 13

13.

The measurements of a triangular field △ABC are BC = 10 cm, AB = 13 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 22000. Calculate the actual length of CA in km.

(i)

1.61 km
(ii)

5.61 km
(iii)

4.61 km
(iv)

3.61 km
(v)

2.61 km

Question 14

14.

The measurements of a triangular field △ABC are BC = 12 cm, AB = 15 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 24000. Calculate the actual area of the plot in sq.km.

(i)

5.18 sq.km
(ii)

4.18 sq.km
(iii)

7.18 sq.km
(iv)

3.18 sq.km
(v)

6.18 sq.km

Question 15

15.

A triangle having an area 65.24 sq.cm is reduced by a scale factor of 0.33. Find the area of its image.

(i)

6.10 sq.cm
(ii)

7.10 sq.cm
(iii)

9.10 sq.cm
(iv)

8.10 sq.cm
(v)

5.10 sq.cm

Question 16

16.

A triangle having an area 72.31 sq.cm is reduced such that the area of its image is 43.99 sq.cm. Find the scale factor.

(i)

2.78
(ii)

1.78
(iii)

7.78
(iv)

8.78
(v)

0.78

Question 17

17.

A rectangle having an area 323.00 sq.cm is reduced by a scale factor of 0.89. Find the area of its image.

(i)

248.85 sq.cm
(ii)

229.85 sq.cm
(iii)

280.85 sq.cm
(iv)

257.85 sq.cm
(v)

255.85 sq.cm

Question 18

18.

A rectangle having an area 133.00 sq.cm is reduced such that the area of its image is 91.62 sq.cm. Find the scale factor.

(i)

0.83
(ii)

1.83
(iii)

2.83
(iv)

7.83
(v)

8.83

Question 19

19.

A model of a ship is made to a scale of 1 : 155. If length of the model ship is 4 m, calculate the length of the ship.

(i)

627.00 m
(ii)

602.00 m
(iii)

646.00 m
(iv)

607.00 m
(v)

620.00 m

Question 20

20.

A model of a ship is made to a scale of 1 : 145. If the length of the ship is 725 m, calculate length of the model ship.

(i)

4.00 m
(ii)

3.00 m
(iii)

5.00 m
(iv)

7.00 m
(v)

6.00 m

Question 21

21.

A model of a ship is made to a scale of 1 : 175. If the area of the deck of the model ship is 144 sq.m, calculate the area of the deck of the ship.

(i)

4640000.00 sq.m
(ii)

4190000.00 sq.m
(iii)

4360000.00 sq.m
(iv)

4410000.00 sq.m
(v)

4550000.00 sq.m

Question 22

22.

A model of a ship is made to a scale of 1 : 95. If the area of the deck of the ship is 902500 sq.m, calculate the area of the deck of the model ship.

(i)

78.00 sq.m
(ii)

98.00 sq.m
(iii)

117.00 sq.m
(iv)

100.00 sq.m

Question 23

23.

A model of a ship is made to a scale of 1 : 160. If the volume of the model ship is 2744 cu.m, calculate the volume of the ship.

(i)

9344456704.00 cu.m
(ii)

12734391296.00 cu.m
(iii)

11939424000.00 cu.m
(iv)

11239424000.00 cu.m
(v)

9739424000.00 cu.m

Question 24

24.

A model of a ship is made to a scale of 1 : 115. If the volume of the ship is 8869743000 cu.m, calculate the volume of the model ship.

(i)

5602.00 cu.m
(ii)

5832.00 cu.m
(iii)

5772.00 cu.m
(iv)

6092.00 cu.m
(v)

6012.00 cu.m

Question 25

25.

The dimensions of the model of a multi-storey building are 8.5 cm ✕ 6 cm ✕ 2.5 cm. If the model is drawn to a scale of 1 : 125, find the actual dimensions of the building.

(i)

1063.5 cm ✕ 751 cm ✕ 312.5 cm
(ii)

1062.5 cm ✕ 750 cm ✕ 312.5 cm
(iii)

1063.5 cm ✕ 750 cm ✕ 312.5 cm
(iv)

1062.5 cm ✕ 751 cm ✕ 312.5 cm
(v)

1062.5 cm ✕ 750 cm ✕ 313.5 cm

Question 26

26.

The dimensions of the model of a multi-storey building are 4.5 cm ✕ 2 cm ✕ 7 cm. If the model is drawn to a scale of 1 : 100, find the floor area of a room of the building whose area in the model is 49 sq.cm.

(i)

44.00 sq.m
(ii)

52.00 sq.m
(iii)

54.00 sq.m
(iv)

46.00 sq.m
(v)

49.00 sq.m

Question 27

27.

The dimensions of the model of a multi-storey building are 6 cm ✕ 9 cm ✕ 7 cm. If the model is drawn to a scale of 1 : 55, find the volume of the room in the model whose actual volume is 681.472 cu.m.

(i)

3976.00 cu.cm
(ii)

4156.00 cu.cm
(iii)

4096.00 cu.cm
(iv)

3966.00 cu.cm
(v)

4236.00 cu.cm

Question 28

28.

A model of building is made with a scale factor of 1 : 30. Find the actual height of the building if the height of the model is 5 cm.

(i)

9.50 m
(ii)

3.50 m
(iii)

1.50 m
(iv)

0.50 m
(v)

2.50 m

Question 29

29.

A model of building is made with a scale factor of 1 : 90. Find the volume of the tank on the top of the model if its actual volume is 46656000 cu.cm.

(i)

64.00 cu.cm
(ii)

65.00 cu.cm
(iii)

63.00 cu.cm
(iv)

66.00 cu.cm
(v)

62.00 cu.cm

Assignment Key