EduSahara™ Worksheet

Question 1

1.

△ABC is a triangle with sides BC = 14 cm, CA = 12 cm and AB = 13 cm. △ABC is enlarged to △A'B'C' such that the smallest side of △A'B'C' is 16.8 cm. Find the scale factor.

(i)

9
5
(ii)

1
(iii)

7
3
(iv)

7
5

Question 2

2.

The ratio of the bases of two triangles ABC and DEF is
8

:

3
.

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

(i)

7

:

3
(ii)

9

:

3
(iii)

8

:

1
(iv)

8

:

5
(v)

3

:

8

Question 3

3.

A triangle having an area 52.15 sq.cm is reduced by a scale factor of 0.40. Find the area of its image.

(i)

9.34 sq.cm
(ii)

8.34 sq.cm
(iii)

10.34 sq.cm
(iv)

6.34 sq.cm
(v)

7.34 sq.cm

Question 4

4.

The measurements of a triangular field △ABC are BC = 8 cm, AB = 11 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 18000. Calculate the actual area of the plot in sq.km.

(i)

0.43 sq.km
(ii)

9.43 sq.km
(iii)

3.43 sq.km
(iv)

2.43 sq.km
(v)

1.43 sq.km

Question 5

5.

The dimensions of the model of a multi-storey building are 7 cm ✕ 7 cm ✕ 7 cm. If the model is drawn to a scale of 1 : 185, find the volume of the room in the model whose actual volume is 405.224 cu.m.

(i)

69.00 cu.cm
(ii)

64.00 cu.cm
(iii)

61.00 cu.cm
(iv)

67.00 cu.cm
(v)

59.00 cu.cm

Question 6

6.

A model of a ship is made to a scale of 1 : 75. If the area of the deck of the ship is 140625 sq.m, calculate the area of the deck of the model ship.

(i)

20.00 sq.m
(ii)

25.00 sq.m
(iii)

28.00 sq.m
(iv)

30.00 sq.m
(v)

22.00 sq.m

Question 7

7.

A model of building is made with a scale factor of 1 : 100. Find the actual height of the building if the height of the model is 5.5 cm.

(i)

3.50 m
(ii)

4.50 m
(iii)

6.50 m
(iv)

7.50 m
(v)

5.50 m

Question 8

8.

Which of the following are true?

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

(i)

{a,c,b}
(ii)

{b,c}
(iii)

{a,b}
(iv)

{d,c}
(v)

{e,f,b}

Question 9

9.

The dimensions of the model of a multi-storey building are 10 cm ✕ 2 cm ✕ 3 cm. If the model is drawn to a scale of 1 : 130, find the floor area of a room of the building whose area in the model is 324 sq.cm.

(i)

520.56 sq.m
(ii)

560.56 sq.m
(iii)

532.56 sq.m
(iv)

547.56 sq.m
(v)

573.56 sq.m

Question 10

10.

The measurements of a triangular field △ABC are BC = 13 cm, AB = 15 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 21000. Calculate the actual length of CA in km.

(i)

4.17 km
(ii)

3.17 km
(iii)

5.17 km
(iv)

6.17 km
(v)

2.17 km

Question 11

11.

AB = 19.00 cm, BC = 17.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 7000. Calculate the area of the field.

(i)

9.58 sq.km
(ii)

3.58 sq.km
(iii)

2.58 sq.km
(iv)

0.58 sq.km
(v)

1.58 sq.km

Question 12

12.

Which of the following are true?

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

(i)

{a,b}
(ii)

{d,c}
(iii)

{d,c,b}
(iv)

{e,a,b}
(v)

{b,c}

Question 13

13.

A model of building is made with a scale factor of 1 : 80. Find the volume of the tank on the top of the model if its actual volume is 512000 cu.cm.

(i)

9.00 cu.cm
(ii)

3.00 cu.cm
(iii)

0.00 cu.cm
(iv)

1.00 cu.cm
(v)

2.00 cu.cm

Question 14

14.

A model of a ship is made to a scale of 1 : 120. If the area of the deck of the model ship is 64 sq.m, calculate the area of the deck of the ship.

(i)

929600.00 sq.m
(ii)

908600.00 sq.m
(iii)

933600.00 sq.m
(iv)

905600.00 sq.m
(v)

921600.00 sq.m

Question 15

15.

Which of the following are true?

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

(i)

{a,b,c}
(ii)

{d,a}
(iii)

{d,a,b}
(iv)

{d,c}
(v)

{d,b}

Question 16

16.

Which of the following are true?

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

(i)

{c,a}
(ii)

{a,b,d}
(iii)

{c,d}
(iv)

{c,b}
(v)

{c,a,b}

Question 17

17.

A model of a ship is made to a scale of 1 : 140. If length of the model ship is 11 m, calculate the length of the ship.

(i)

1260.00 m
(ii)

1790.00 m
(iii)

1610.00 m
(iv)

1510.00 m
(v)

1540.00 m

Question 18

18.

The dimensions of the model of a multi-storey building are 1 cm ✕ 7 cm ✕ 10 cm. If the model is drawn to a scale of 1 : 140, find the actual dimensions of the building.

(i)

140 cm ✕ 981 cm ✕ 1400 cm
(ii)

141 cm ✕ 981 cm ✕ 1400 cm
(iii)

141 cm ✕ 980 cm ✕ 1400 cm
(iv)

140 cm ✕ 980 cm ✕ 1400 cm
(v)

140 cm ✕ 980 cm ✕ 1401 cm

Question 19

19.

A model of a ship is made to a scale of 1 : 55. If the volume of the model ship is 4913 cu.m, calculate the volume of the ship.

(i)

800400375.00 cu.m
(ii)

822400375.00 cu.m
(iii)

795400375.00 cu.m
(iv)

817400375.00 cu.m
(v)

834400375.00 cu.m

Question 20

20.

Which of the following are true?

a)	Area of the union of two polygonal region is not equal to the sum of the individual area.
b)	A polygonal region can be divided into a finite number of triangles in a unique way.
c)	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.
d)	Area of the union of two polygonal region is the sum of the individual area.

(i)

{a,c}
(ii)

{b,d,a}
(iii)

{b,a}
(iv)

{b,c,a}
(v)

{d,c}

Question 21

21.

Which of the following are true?

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

(i)

{a,b}
(ii)

{c,d}
(iii)

{a,c,e}
(iv)

{a,b,d}
(v)

{b,d,e}

Question 22

22.

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

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

(i)

{a,c}
(ii)

{b,c,a}
(iii)

{b,d,a}
(iv)

{b,a}
(v)

{d,c}

Question 23

23.

A triangle having an area 83.03 sq.cm is enlarged such that the area of its image is 113.66 sq.cm. Find the scale factor.

(i)

1.17
(ii)

0.17
(iii)

9.17
(iv)

3.17
(v)

2.17

Question 24

24.

△ABC is a triangle with sides BC = 12 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 22.5 cm. Find the corresponding lengths of the enlarged triangle △A'B'C'.

(i)

28 cm, 23.5 cm, 25.75 cm
(ii)

27 cm, 22.5 cm, 24.75 cm
(iii)

29 cm, 24.5 cm, 26.75 cm
(iv)

25 cm, 20.5 cm, 22.75 cm
(v)

26 cm, 21.5 cm, 23.75 cm

Question 25

25.

A model of a ship is made to a scale of 1 : 75. If the volume of the ship is 52734375 cu.m, calculate the volume of the model ship.

(i)

125.00 cu.m
(ii)

128.00 cu.m
(iii)

117.00 cu.m
(iv)

137.00 cu.m
(v)

101.00 cu.m

Assignment Key