EduSahara™ Worksheet

Question 1

1.

A triangle having an area 63.17 sq.cm is enlarged by a scale factor of 1.80. Find the area of its image.

(i)

221.68 sq.cm
(ii)

204.68 sq.cm
(iii)

196.68 sq.cm
(iv)

227.68 sq.cm
(v)

179.68 sq.cm

Question 2

2.

The dimensions of the model of a multi-storey building are 9.5 cm ✕ 3 cm ✕ 3 cm. If the model is drawn to a scale of 1 : 85, find the actual dimensions of the building.

(i)

807.5 cm ✕ 255 cm ✕ 255 cm
(ii)

807.5 cm ✕ 255 cm ✕ 256 cm
(iii)

808.5 cm ✕ 255 cm ✕ 255 cm
(iv)

808.5 cm ✕ 256 cm ✕ 255 cm
(v)

807.5 cm ✕ 256 cm ✕ 255 cm

Question 3

3.

A model of a ship is made to a scale of 1 : 110. If the volume of the model ship is 512 cu.m, calculate the volume of the ship.

(i)

657472000.00 cu.m
(ii)

686472000.00 cu.m
(iii)

681472000.00 cu.m
(iv)

678472000.00 cu.m
(v)

707472000.00 cu.m

Question 4

4.

A triangle having an area 59.92 sq.cm is enlarged such that the area of its image is 82.03 sq.cm. Find the scale factor.

(i)

9.17
(ii)

1.17
(iii)

3.17
(iv)

2.17
(v)

0.17

Question 5

5.

The measurements of a triangular field △ABC are BC = 14 cm, AB = 7 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)

2.82 sq.km
(ii)

3.82 sq.km
(iii)

1.82 sq.km
(iv)

0.82 sq.km
(v)

4.82 sq.km

Question 6

6.

Which of the following are true?

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

(i)

{c,f}
(ii)

{a,b}
(iii)

{b,f}
(iv)

{d,e,b}
(v)

{a,f,b}

Question 7

7.

△ABC is a triangle with sides BC = 15 cm, CA = 13 cm and AB = 10 cm. △ABC is enlarged to △A'B'C' such that the smallest side of △A'B'C' is 11.25 cm. Find the corresponding lengths of the enlarged triangle △A'B'C'.

(i)

15.88 cm, 13.62 cm, 10.25 cm
(ii)

17.88 cm, 15.62 cm, 12.25 cm
(iii)

16.88 cm, 14.62 cm, 11.25 cm
(iv)

14.88 cm, 12.62 cm, 9.25 cm
(v)

18.88 cm, 16.62 cm, 13.25 cm

Question 8

8.

A rectangle having an area 84.00 sq.cm is reduced such that the area of its image is 1.65 sq.cm. Find the scale factor.

(i)

1.14
(ii)

7.14
(iii)

2.14
(iv)

0.14
(v)

8.14

Question 9

9.

The ratio of the bases of two triangles ABC and DEF is
9

:

8
.

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

(i)

9

:

5
(ii)

8

:

9
(iii)

9

:

11
(iv)

10

:

8
(v)

8

:

8

Question 10

10.

The measurements of a triangular field △ABC are BC = 14 cm, AB = 11 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 17000. Calculate the actual length of CA in km.

(i)

5.03 km
(ii)

3.03 km
(iii)

4.03 km
(iv)

2.03 km
(v)

1.03 km

Question 11

11.

A model of a ship is made to a scale of 1 : 135. If the length of the ship is 1890 m, calculate length of the model ship.

(i)

9.00 m
(ii)

11.00 m
(iii)

19.00 m
(iv)

14.00 m
(v)

17.00 m

Question 12

12.

A rectangle having an area 180.00 sq.cm is enlarged by a scale factor of 1.29. Find the area of its image.

(i)

293.54 sq.cm
(ii)

284.54 sq.cm
(iii)

299.54 sq.cm
(iv)

325.54 sq.cm
(v)

307.54 sq.cm

Question 13

13.

△ABC is a triangle with sides BC = 13 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 90 cm. Find the scale factor.

(i)

12
(ii)

9
(iii)

6
(iv)

10
(v)

8

Question 14

14.

A model of building is made with a scale factor of 1 : 50. Find the volume of the tank on the top of the model if its actual volume is 125000000 cu.cm.

(i)

1002.00 cu.cm
(ii)

998.00 cu.cm
(iii)

999.00 cu.cm
(iv)

1000.00 cu.cm
(v)

1001.00 cu.cm

Question 15

15.

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)

{d,a}
(ii)

{d,c}
(iii)

{d,b}
(iv)

{a,b,c}
(v)

{d,a,b}

Question 16

16.

AB = 18.00 cm, BC = 16.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 19000. Calculate the area of the field.

(i)

9.40 sq.km
(ii)

12.40 sq.km
(iii)

11.40 sq.km
(iv)

10.40 sq.km
(v)

8.40 sq.km

Question 17

17.

The dimensions of the model of a multi-storey building are 4 cm ✕ 7 cm ✕ 6.5 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 121.2874 cu.m.

(i)

711.00 cu.cm
(ii)

712.00 cu.cm
(iii)

729.00 cu.cm
(iv)

743.00 cu.cm

Question 18

18.

Which of the following are true?

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

(i)

{a,c,e}
(ii)

{b,a,c}
(iii)

{b,d,e}
(iv)

{d,c}
(v)

{b,a}

Question 19

19.

Which of the following are true?

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

(i)

{d,a,b}
(ii)

{a,b}
(iii)

{c,e}
(iv)

{b,e}
(v)

{c,e,b}

Question 20

20.

AB = 18.00 cm, BC = 11.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 11000. Calculate the diagonal distance of the field.

(i)

3.32 km
(ii)

0.32 km
(iii)

4.32 km
(iv)

2.32 km
(v)

1.32 km

Question 21

21.

A model of a ship is made to a scale of 1 : 115. If the area of the deck of the model ship is 121 sq.m, calculate the area of the deck of the ship.

(i)

1720225.00 sq.m
(ii)

1540225.00 sq.m
(iii)

1650225.00 sq.m
(iv)

1600225.00 sq.m
(v)

1370225.00 sq.m

Question 22

22.

A model of a ship is made to a scale of 1 : 115. If length of the model ship is 17 m, calculate the length of the ship.

(i)

1725.00 m
(ii)

2095.00 m
(iii)

1835.00 m
(iv)

2235.00 m
(v)

1955.00 m

Question 23

23.

Which of the following are true?

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

(i)

{c,a}
(ii)

{c,d}
(iii)

{c,a,b}
(iv)

{c,b}
(v)

{a,b,d}

Question 24

24.

A model of building is made with a scale factor of 1 : 70. Find the actual height of the building if the height of the model is 3.5 cm.

(i)

1.45 m
(ii)

0.45 m
(iii)

4.45 m
(iv)

3.45 m
(v)

2.45 m

Question 25

25.

A model of a ship is made to a scale of 1 : 170. If the volume of the ship is 1685159000 cu.m, calculate the volume of the model ship.

(i)

368.00 cu.m
(ii)

327.00 cu.m
(iii)

343.00 cu.m
(iv)

326.00 cu.m
(v)

351.00 cu.m

Assignment Key