EduSahara™ Worksheet

Question 1

1.

A rectangle having an area 300.00 sq.cm is enlarged such that the area of its image is 675.00 sq.cm. Find the scale factor.

(i)

1.5
(ii)

0.5
(iii)

9.5
(iv)

3.5
(v)

2.5

Question 2

2.

The dimensions of the model of a multi-storey building are 10 cm ✕ 7 cm ✕ 5.5 cm. If the model is drawn to a scale of 1 : 130, find the actual dimensions of the building.

(i)

1301 cm ✕ 910 cm ✕ 715 cm
(ii)

1300 cm ✕ 910 cm ✕ 715 cm
(iii)

1300 cm ✕ 910 cm ✕ 716 cm
(iv)

1301 cm ✕ 911 cm ✕ 715 cm
(v)

1300 cm ✕ 911 cm ✕ 715 cm

Question 3

3.

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 6 cm.

(i)

2.80 m
(ii)

3.80 m
(iii)

1.80 m
(iv)

9.80 m
(v)

0.80 m

Question 4

4.

A rectangle having an area 221.00 sq.cm is enlarged by a scale factor of 1.33. Find the area of its image.

(i)

403.93 sq.cm
(ii)

390.93 sq.cm
(iii)

397.93 sq.cm
(iv)

376.93 sq.cm
(v)

365.93 sq.cm

Question 5

5.

Which of the following are true?

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

(i)

{b,c,a}
(ii)

{b,d,a}
(iii)

{a,c}
(iv)

{d,c}
(v)

{b,a}

Question 6

6.

The dimensions of the model of a multi-storey building are 5.5 cm ✕ 2 cm ✕ 5.5 cm. If the model is drawn to a scale of 1 : 50, find the floor area of a room of the building whose area in the model is 121 sq.cm.

(i)

30.25 sq.m
(ii)

35.25 sq.m
(iii)

25.25 sq.m
(iv)

27.25 sq.m
(v)

33.25 sq.m

Question 7

7.

AB = 19.00 cm, BC = 11.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 8000. Calculate the area of the field.

(i)

0.34 sq.km
(ii)

2.34 sq.km
(iii)

1.34 sq.km
(iv)

3.34 sq.km
(v)

9.34 sq.km

Question 8

8.

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)

{b,d,e}
(ii)

{a,c,e}
(iii)

{a,b}
(iv)

{c,d}
(v)

{a,b,d}

Question 9

9.

A model of building is made with a scale factor of 1 : 70. Find the volume of the tank on the top of the model if its actual volume is 57066625 cu.cm.

(i)

168.38 cu.cm
(ii)

165.38 cu.cm
(iii)

167.38 cu.cm
(iv)

166.38 cu.cm
(v)

164.38 cu.cm

Question 10

10.

Which of the following are true?

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

(i)

{a,c}
(ii)

{d,e,c}
(iii)

{b,f}
(iv)

{c,f}
(v)

{a,f,c}

Question 11

11.

Which of the following are true?

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

(i)

{a,c}
(ii)

{b,d}
(iii)

{c,d}
(iv)

{b,d,c}
(v)

{e,a,c}

Question 12

12.

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

:

9
.

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

(i)

7

:

9
(ii)

9

:

8
(iii)

8

:

12
(iv)

8

:

7
(v)

9

:

9

Question 13

13.

A model of a ship is made to a scale of 1 : 75. If the volume of the model ship is 64 cu.m, calculate the volume of the ship.

(i)

27000000.00 cu.m
(ii)

26800000.00 cu.m
(iii)

28300000.00 cu.m
(iv)

25400000.00 cu.m
(v)

29500000.00 cu.m

Question 14

14.

A model of a ship is made to a scale of 1 : 145. If the length of the ship is 2610 m, calculate length of the model ship.

(i)

15.00 m
(ii)

21.00 m
(iii)

23.00 m
(iv)

13.00 m
(v)

18.00 m

Question 15

15.

△ABC is a triangle with sides BC = 12 cm, CA = 11 cm and AB = 10 cm. △ABC is enlarged to △A'B'C' such that the smallest side of △A'B'C' is 15 cm. Find the scale factor.

(i)

1
2
(ii)

3
2
(iii)

3
4
(iv)

3
(v)

5
2

Question 16

16.

The dimensions of the model of a multi-storey building are 5 cm ✕ 9.5 cm ✕ 9.5 cm. If the model is drawn to a scale of 1 : 125, find the volume of the room in the model whose actual volume is 8000 cu.m.

(i)

4146.00 cu.cm
(ii)

3856.00 cu.cm
(iii)

3926.00 cu.cm
(iv)

4356.00 cu.cm
(v)

4096.00 cu.cm

Question 17

17.

The measurements of a triangular field △ABC are BC = 5 cm, AB = 9 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 17000. Calculate the actual area of the plot in sq.km.

(i)

1.65 sq.km
(ii)

7.65 sq.km
(iii)

8.65 sq.km
(iv)

2.65 sq.km
(v)

0.65 sq.km

Question 18

18.

Which of the following are true?

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

(i)

{c,b}
(ii)

{a,b,d}
(iii)

{c,d}
(iv)

{c,a}
(v)

{c,a,b}

Question 19

19.

A triangle having an area 28.57 sq.cm is reduced such that the area of its image is 2.4 sq.cm. Find the scale factor.

(i)

8.29
(ii)

7.29
(iii)

0.29
(iv)

2.29
(v)

1.29

Question 20

20.

A model of a ship is made to a scale of 1 : 115. If the area of the deck of the model ship is 16 sq.m, calculate the area of the deck of the ship.

(i)

185600.00 sq.m
(ii)

211600.00 sq.m
(iii)

194600.00 sq.m
(iv)

239600.00 sq.m
(v)

226600.00 sq.m

Question 21

21.

The measurements of a triangular field △ABC are BC = 13 cm, AB = 6 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 21000. Calculate the actual length of CA in km.

(i)

5.01 km
(ii)

4.01 km
(iii)

2.01 km
(iv)

1.01 km
(v)

3.01 km

Question 22

22.

A model of a ship is made to a scale of 1 : 155. If the volume of the ship is 3723875000 cu.m, calculate the volume of the model ship.

(i)

1120.00 cu.m
(ii)

1050.00 cu.m
(iii)

1000.00 cu.m
(iv)

960.00 cu.m
(v)

840.00 cu.m

Question 23

23.

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 : 15000. Calculate the diagonal distance of the field.

(i)

1.82 km
(ii)

3.82 km
(iii)

5.82 km
(iv)

2.82 km
(v)

4.82 km

Question 24

24.

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 sides are equal.
d)	The corresponding angles are equal.

(i)

{a,c,b}
(ii)

{a,d,b}
(iii)

{b,d}
(iv)

{c,d}
(v)

{a,b}

Question 25

25.

A triangle having an area 25.22 sq.cm is enlarged by a scale factor of 3.00. Find the area of its image.

(i)

212.96 sq.cm
(ii)

226.96 sq.cm
(iii)

239.96 sq.cm
(iv)

251.96 sq.cm
(v)

200.96 sq.cm

Assignment Key