EduSahara™ Worksheet

Question 1

1.

Which of the following are true?

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

(i)

{a,b,c}
(ii)

{d,a,b}
(iii)

{d,c}
(iv)

{d,b}
(v)

{d,a}

Question 2

2.

Which of the following are true?

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

(i)

{c,d}
(ii)

{b,d,a}
(iii)

{b,a}
(iv)

{a,d}
(v)

{e,f,a}

Question 3

3.

The ratio of the bases of two triangles ABC and DEF is
7

:

3
.

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

(i)

6

:

3
(ii)

3

:

7
(iii)

7

:

5
(iv)

8

:

3
(v)

7

:

0

Question 4

4.

The measurements of a triangular field △ABC are BC = 13 cm, AB = 5 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 20000. Calculate the actual length of CA in km.

(i)

0.79 km
(ii)

3.79 km
(iii)

1.79 km
(iv)

2.79 km
(v)

4.79 km

Question 5

5.

A model of a ship is made to a scale of 1 : 100. If the length of the ship is 400 m, calculate length of the model ship.

(i)

2.00 m
(ii)

3.00 m
(iii)

6.00 m
(iv)

5.00 m
(v)

4.00 m

Question 6

6.

The dimensions of the model of a multi-storey building are 8.5 cm ✕ 2 cm ✕ 7 cm. If the model is drawn to a scale of 1 : 105, find the volume of the room in the model whose actual volume is 6751.269 cu.m.

(i)

5832.00 cu.cm
(ii)

5602.00 cu.cm
(iii)

5782.00 cu.cm
(iv)

5912.00 cu.cm
(v)

6102.00 cu.cm

Question 7

7.

A model of a ship is made to a scale of 1 : 60. If the volume of the model ship is 4913 cu.m, calculate the volume of the ship.

(i)

1321208000.00 cu.m
(ii)

941208000.00 cu.m
(iii)

1191208000.00 cu.m
(iv)

1061208000.00 cu.m
(v)

1011208000.00 cu.m

Question 8

8.

Which of the following are true?

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

(i)

{d,c}
(ii)

{b,d,e}
(iii)

{b,a,c}
(iv)

{b,a}
(v)

{a,c,e}

Question 9

9.

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 5832000 cu.cm.

(i)

8.00 cu.cm
(ii)

10.00 cu.cm
(iii)

9.00 cu.cm
(iv)

6.00 cu.cm
(v)

7.00 cu.cm

Question 10

10.

A rectangle having an area 342.00 sq.cm is reduced by a scale factor of 0.43. Find the area of its image.

(i)

58.24 sq.cm
(ii)

66.24 sq.cm
(iii)

63.24 sq.cm
(iv)

68.24 sq.cm
(v)

60.24 sq.cm

Question 11

11.

△ABC is a triangle with sides BC = 10 cm, CA = 15 cm and AB = 13 cm. △ABC is reduced to △A'B'C' such that the smallest side of △A'B'C' is 1.43 cm. Find the corresponding lengths of the reduced triangle △A'B'C'.

(i)

2.43 cm, 3.14 cm, 2.86 cm
(ii)

0.43 cm, 1.14 cm, 0.86 cm
(iii)

1.43 cm, 2.14 cm, 1.86 cm
(iv)

3.43 cm, 4.14 cm, 3.86 cm
(v)

9.43 cm, 0.14 cm, 9.86 cm

Question 12

12.

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

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

(i)

{b,d}
(ii)

{a,d,c}
(iii)

{a,c}
(iv)

{a,b,c}
(v)

{c,d}

Question 13

13.

The dimensions of the model of a multi-storey building are 2.5 cm ✕ 8.5 cm ✕ 2 cm. If the model is drawn to a scale of 1 : 75, find the floor area of a room of the building whose area in the model is 256 sq.cm.

(i)

150.00 sq.m
(ii)

137.00 sq.m
(iii)

126.00 sq.m
(iv)

157.00 sq.m
(v)

144.00 sq.m

Question 14

14.

A model of a ship is made to a scale of 1 : 70. If the area of the deck of the model ship is 4 sq.m, calculate the area of the deck of the ship.

(i)

21000.00 sq.m
(ii)

18000.00 sq.m
(iii)

19800.00 sq.m
(iv)

18900.00 sq.m
(v)

19600.00 sq.m

Question 15

15.

The measurements of a triangular field △ABC are BC = 11 cm, AB = 14 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 19000. Calculate the actual area of the plot in sq.km.

(i)

2.78 sq.km
(ii)

0.78 sq.km
(iii)

3.78 sq.km
(iv)

1.78 sq.km
(v)

4.78 sq.km

Question 16

16.

The dimensions of the model of a multi-storey building are 10 cm ✕ 8 cm ✕ 1.5 cm. If the model is drawn to a scale of 1 : 200, find the actual dimensions of the building.

(i)

2001 cm ✕ 1600 cm ✕ 300 cm
(ii)

2000 cm ✕ 1600 cm ✕ 300 cm
(iii)

2001 cm ✕ 1601 cm ✕ 300 cm
(iv)

2000 cm ✕ 1600 cm ✕ 301 cm
(v)

2000 cm ✕ 1601 cm ✕ 300 cm

Question 17

17.

AB = 6.00 cm, BC = 5.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 10000. Calculate the diagonal distance of the field.

(i)

0.78 km
(ii)

7.78 km
(iii)

8.78 km
(iv)

2.78 km
(v)

1.78 km

Question 18

18.

A model of a ship is made to a scale of 1 : 175. If the volume of the ship is 669921875 cu.m, calculate the volume of the model ship.

(i)

141.00 cu.m
(ii)

113.00 cu.m
(iii)

125.00 cu.m
(iv)

120.00 cu.m

Question 19

19.

△ABC is a triangle with sides BC = 10 cm, CA = 11 cm and AB = 13 cm. △ABC is reduced to △A'B'C' such that the smallest side of △A'B'C' is 5.71 cm. Find the scale factor.

(i)

4
5
(ii)

4
7
(iii)

6
7
(iv)

2
7
(v)

4
9

Question 20

20.

A model of building is made with a scale factor of 1 : 60. Find the actual height of the building if the height of the model is 9.5 cm.

(i)

4.70 m
(ii)

5.70 m
(iii)

6.70 m
(iv)

3.70 m
(v)

7.70 m

Question 21

21.

A model of a ship is made to a scale of 1 : 155. If length of the model ship is 2 m, calculate the length of the ship.

(i)

310.00 m
(ii)

338.00 m
(iii)

317.00 m
(iv)

294.00 m

Question 22

22.

A triangle having an area 29.39 sq.cm is reduced such that the area of its image is 7.35 sq.cm. Find the scale factor.

(i)

7.5
(ii)

0.5
(iii)

2.5
(iv)

1.5
(v)

8.5

Question 23

23.

A triangle having an area 55.53 sq.cm is reduced by a scale factor of 0.62. Find the area of its image.

(i)

21.35 sq.cm
(ii)

24.35 sq.cm
(iii)

16.35 sq.cm
(iv)

18.35 sq.cm
(v)

26.35 sq.cm

Question 24

24.

A rectangle having an area 272.00 sq.cm is reduced such that the area of its image is 29.62 sq.cm. Find the scale factor.

(i)

2.33
(ii)

0.33
(iii)

7.33
(iv)

8.33
(v)

1.33

Question 25

25.

A model of a ship is made to a scale of 1 : 120. If the area of the deck of the ship is 2073600 sq.m, calculate the area of the deck of the model ship.

(i)

156.00 sq.m
(ii)

149.00 sq.m
(iii)

144.00 sq.m
(iv)

141.00 sq.m
(v)

120.00 sq.m

Assignment Key