EduSahara™ Worksheet

Question 1

1.

Which of the following are true?

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

(i)

{d,a,b}
(ii)

{b,e}
(iii)

{a,b}
(iv)

{c,e,b}
(v)

{c,e}

Question 2

2.

AB = 17.00 cm, BC = 8.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 7000. Calculate the diagonal distance of the field.

(i)

9.32 km
(ii)

2.32 km
(iii)

3.32 km
(iv)

1.32 km
(v)

0.32 km

Question 3

3.

A triangle having an area 55.32 sq.cm is enlarged such that the area of its image is 124.46 sq.cm. Find the scale factor.

(i)

2.5
(ii)

9.5
(iii)

3.5
(iv)

0.5
(v)

1.5

Question 4

4.

A model of a ship is made to a scale of 1 : 80. If the area of the deck of the model ship is 64 sq.m, calculate the area of the deck of the ship.

(i)

437600.00 sq.m
(ii)

409600.00 sq.m
(iii)

392600.00 sq.m
(iv)

414600.00 sq.m
(v)

385600.00 sq.m

Question 5

5.

The measurements of a triangular field △ABC are BC = 5 cm, AB = 8 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 25000. Calculate the actual area of the plot in sq.km.

(i)

3.25 sq.km
(ii)

2.25 sq.km
(iii)

1.25 sq.km
(iv)

9.25 sq.km
(v)

0.25 sq.km

Question 6

6.

The measurements of a triangular field △ABC are BC = 13 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)

1.89 km
(ii)

3.89 km
(iii)

0.89 km
(iv)

4.89 km
(v)

2.89 km

Question 7

7.

The dimensions of the model of a multi-storey building are 9 cm ✕ 8 cm ✕ 1 cm. If the model is drawn to a scale of 1 : 85, find the volume of the room in the model whose actual volume is 39.304 cu.m.

(i)

61.00 cu.cm
(ii)

59.00 cu.cm
(iii)

69.00 cu.cm
(iv)

67.00 cu.cm
(v)

64.00 cu.cm

Question 8

8.

A model of a ship is made to a scale of 1 : 70. If length of the model ship is 2 m, calculate the length of the ship.

(i)

122.00 m
(ii)

127.00 m
(iii)

146.00 m
(iv)

140.00 m
(v)

167.00 m

Question 9

9.

△ABC is a triangle with sides BC = 11 cm, CA = 12 cm and AB = 14 cm. △ABC is enlarged to △A'B'C' such that the smallest side of △A'B'C' is 27.5 cm. Find the corresponding lengths of the enlarged triangle △A'B'C'.

(i)

25.5 cm, 28 cm, 33 cm
(ii)

27.5 cm, 30 cm, 35 cm
(iii)

28.5 cm, 31 cm, 36 cm
(iv)

29.5 cm, 32 cm, 37 cm
(v)

26.5 cm, 29 cm, 34 cm

Question 10

10.

A model of a ship is made to a scale of 1 : 195. If the volume of the ship is 7414875000 cu.m, calculate the volume of the model ship.

(i)

1000.00 cu.m
(ii)

870.00 cu.m
(iii)

1160.00 cu.m
(iv)

960.00 cu.m
(v)

1120.00 cu.m

Question 11

11.

Which of the following are true?

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

(i)

{d,c}
(ii)

{b,a}
(iii)

{b,c,a}
(iv)

{a,c}
(v)

{e,f,a}

Question 12

12.

A rectangle having an area 252.00 sq.cm is reduced by a scale factor of 0.62. Find the area of its image.

(i)

101.87 sq.cm
(ii)

96.87 sq.cm
(iii)

91.87 sq.cm
(iv)

93.87 sq.cm
(v)

99.87 sq.cm

Question 13

13.

△ABC is a triangle with sides BC = 13 cm, CA = 15 cm and AB = 12 cm. △ABC is reduced to △A'B'C' such that the smallest side of △A'B'C' is 8.57 cm. Find the scale factor.

(i)

3
7
(ii)

5
7
(iii)

5
9
(iv)

1

Question 14

14.

A rectangle having an area 56.00 sq.cm is reduced such that the area of its image is 6.10 sq.cm. Find the scale factor.

(i)

7.33
(ii)

2.33
(iii)

0.33
(iv)

8.33
(v)

1.33

Question 15

15.

A model of a ship is made to a scale of 1 : 150. If the length of the ship is 2250 m, calculate length of the model ship.

(i)

18.00 m
(ii)

15.00 m
(iii)

10.00 m
(iv)

20.00 m
(v)

12.00 m

Question 16

16.

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 6 cm.

(i)

2.60 m
(ii)

1.60 m
(iii)

4.60 m
(iv)

5.60 m
(v)

3.60 m

Question 17

17.

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

:

7
.

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

(i)

9

:

7
(ii)

11

:

7
(iii)

10

:

10
(iv)

10

:

4
(v)

7

:

10

Question 18

18.

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 64000000 cu.cm.

(i)

125.00 cu.cm
(ii)

124.00 cu.cm
(iii)

123.00 cu.cm
(iv)

126.00 cu.cm
(v)

127.00 cu.cm

Question 19

19.

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)	Area of the union of two polygonal region is 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)

{b,d,a}
(ii)

{b,a}
(iii)

{a,d}
(iv)

{b,c,a}
(v)

{c,d}

Question 20

20.

A triangle having an area 55.8 sq.cm is reduced by a scale factor of 0.67. Find the area of its image.

(i)

22.05 sq.cm
(ii)

20.05 sq.cm
(iii)

30.05 sq.cm
(iv)

25.05 sq.cm
(v)

28.05 sq.cm

Question 21

21.

The dimensions of the model of a multi-storey building are 9.5 cm ✕ 1.5 cm ✕ 1 cm. If the model is drawn to a scale of 1 : 190, find the floor area of a room of the building whose area in the model is 25 sq.cm.

(i)

95.25 sq.m
(ii)

85.25 sq.m
(iii)

93.25 sq.m
(iv)

90.25 sq.m
(v)

87.25 sq.m

Question 22

22.

A model of a ship is made to a scale of 1 : 70. If the volume of the model ship is 2197 cu.m, calculate the volume of the ship.

(i)

768571000.00 cu.m
(ii)

746571000.00 cu.m
(iii)

753571000.00 cu.m
(iv)

735571000.00 cu.m
(v)

769571000.00 cu.m

Question 23

23.

AB = 19.00 cm, BC = 18.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 5000. Calculate the area of the field.

(i)

1.85 sq.km
(ii)

8.86 sq.km
(iii)

7.86 sq.km
(iv)

0.85 sq.km
(v)

2.85 sq.km

Question 24

24.

Which of the following are true?

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

(i)

{a,b}
(ii)

{a,b,c}
(iii)

{a,c}
(iv)

{a,d}
(v)

{b,c,d}

Question 25

25.

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

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

(i)

{c,d,a}
(ii)

{a,b}
(iii)

{d,b}
(iv)

{c,b,a}
(v)

{c,a}

Assignment Key