EduSahara™ Worksheet

Question 1

1.

Which of the following are true?

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

(i)

{e,c}
(ii)

{a,e,d}
(iii)

{a,b}
(iv)

{a,b,c}
(v)

{b,c,d}

Question 2

2.

AB = 15.00 cm, BC = 10.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 21000. Calculate the area of the field.

(i)

6.62 sq.km
(ii)

7.62 sq.km
(iii)

5.62 sq.km
(iv)

4.62 sq.km
(v)

8.62 sq.km

Question 3

3.

Which of the following are true?

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

(i)

{d,c,b}
(ii)

{b,c}
(iii)

{e,a,b}
(iv)

{d,c}
(v)

{a,b}

Question 4

4.

A triangle having an area 136.79 sq.cm is reduced such that the area of its image is 44.44 sq.cm. Find the scale factor.

(i)

1.57
(ii)

2.57
(iii)

8.57
(iv)

0.57
(v)

7.57

Question 5

5.

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

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

(i)

{b,d,a}
(ii)

{b,c,a}
(iii)

{b,a}
(iv)

{d,c}
(v)

{a,c}

Question 6

6.

The ratio of the bases of two triangles ABC and DEF is
6

:

10
.

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

(i)

7

:

10
(ii)

10

:

6
(iii)

5

:

10
(iv)

6

:

13
(v)

6

:

7

Question 7

7.

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,c,a}
(iii)

{d,c}
(iv)

{b,a}
(v)

{b,d,a}

Question 8

8.

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 3.5 cm.

(i)

0.05 m
(ii)

1.05 m
(iii)

2.05 m
(iv)

9.05 m
(v)

3.05 m

Question 9

9.

A model of a ship is made to a scale of 1 : 85. If the length of the ship is 1105 m, calculate length of the model ship.

(i)

16.00 m
(ii)

13.00 m
(iii)

10.00 m
(iv)

18.00 m
(v)

8.00 m

Question 10

10.

AB = 15.00 cm, BC = 5.00 cm are the measurements of a rectangular field of land ABCD on a map drawn to a scale of 1 : 7000. Calculate the diagonal distance of the field.

(i)

9.11 km
(ii)

2.11 km
(iii)

0.11 km
(iv)

3.11 km
(v)

1.11 km

Question 11

11.

A model of a ship is made to a scale of 1 : 125. If the area of the deck of the model ship is 225 sq.m, calculate the area of the deck of the ship.

(i)

3515625.00 sq.m
(ii)

3565625.00 sq.m
(iii)

3675625.00 sq.m
(iv)

3375625.00 sq.m
(v)

3435625.00 sq.m

Question 12

12.

The measurements of a triangular field △ABC are BC = 7 cm, AB = 13 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 15000. Calculate the actual length of CA in km.

(i)

0.21 km
(ii)

4.21 km
(iii)

2.21 km
(iv)

3.21 km
(v)

1.21 km

Question 13

13.

A model of a ship is made to a scale of 1 : 200. If the volume of the model ship is 5832 cu.m, calculate the volume of the ship.

(i)

46396000000.00 cu.m
(ii)

46656000000.00 cu.m
(iii)

46776000000.00 cu.m
(iv)

46786000000.00 cu.m
(v)

46526000000.00 cu.m

Question 14

14.

Which of the following are true?

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

(i)

{c,f}
(ii)

{d,e,c}
(iii)

{a,f,c}
(iv)

{b,f}
(v)

{a,c}

Question 15

15.

A rectangle having an area 270.00 sq.cm is reduced such that the area of its image is 151.88 sq.cm. Find the scale factor.

(i)

8.75
(ii)

7.75
(iii)

1.75
(iv)

2.75
(v)

0.75

Question 16

16.

△ABC is a triangle with sides BC = 13 cm, CA = 12 cm and AB = 11 cm. △ABC is reduced to △A'B'C' such that the smallest side of △A'B'C' is 7.33 cm. Find the scale factor.

(i)

6
11
(ii)

4
9
(iii)

2
3
(iv)

6
7
(v)

8
9

Question 17

17.

A model of a ship is made to a scale of 1 : 175. If length of the model ship is 18 m, calculate the length of the ship.

(i)

2880.00 m
(ii)

3150.00 m
(iii)

3400.00 m
(iv)

3190.00 m
(v)

2970.00 m

Question 18

18.

A triangle having an area 87.81 sq.cm is reduced by a scale factor of 0.86. Find the area of its image.

(i)

69.95 sq.cm
(ii)

64.95 sq.cm
(iii)

59.95 sq.cm
(iv)

67.95 sq.cm
(v)

61.95 sq.cm

Question 19

19.

Which of the following are true?

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

(i)

{b,c,d}
(ii)

{a,c}
(iii)

{a,b,c}
(iv)

{a,d}
(v)

{a,b}

Question 20

20.

The dimensions of the model of a multi-storey building are 4 cm ✕ 1 cm ✕ 1 cm. If the model is drawn to a scale of 1 : 55, find the actual dimensions of the building.

(i)

221 cm ✕ 56 cm ✕ 55 cm
(ii)

220 cm ✕ 56 cm ✕ 55 cm
(iii)

220 cm ✕ 55 cm ✕ 56 cm
(iv)

220 cm ✕ 55 cm ✕ 55 cm
(v)

221 cm ✕ 55 cm ✕ 55 cm

Question 21

21.

Which of the following are true?

a)	Any two triangles are similar if the corresponding angles are equal.
b)	Any two triangles are similar if the corresponding sides are proportional.
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 22

22.

△ABC is a triangle with sides BC = 14 cm, CA = 10 cm and AB = 13 cm. △ABC is enlarged to △A'B'C' such that the smallest side of △A'B'C' is 17.5 cm. Find the corresponding lengths of the enlarged triangle △A'B'C'.

(i)

24.5 cm, 17.5 cm, 22.75 cm
(ii)

22.5 cm, 15.5 cm, 20.75 cm
(iii)

25.5 cm, 18.5 cm, 23.75 cm
(iv)

26.5 cm, 19.5 cm, 24.75 cm
(v)

23.5 cm, 16.5 cm, 21.75 cm

Question 23

23.

The dimensions of the model of a multi-storey building are 4.5 cm ✕ 2.5 cm ✕ 2.5 cm. If the model is drawn to a scale of 1 : 160, find the floor area of a room of the building whose area in the model is 49 sq.cm.

(i)

112.44 sq.m
(ii)

117.44 sq.m
(iii)

125.44 sq.m
(iv)

143.44 sq.m
(v)

142.44 sq.m

Question 24

24.

The measurements of a triangular field △ABC are BC = 6 cm, AB = 14 cm and ∠ABC = 90° on a map drawn to a scale of 1 : 23000. Calculate the actual area of the plot in sq.km.

(i)

3.22 sq.km
(ii)

1.22 sq.km
(iii)

4.22 sq.km
(iv)

2.22 sq.km
(v)

0.22 sq.km

Question 25

25.

A model of building is made with a scale factor of 1 : 40. Find the volume of the tank on the top of the model if its actual volume is 512000 cu.cm.

(i)

7.00 cu.cm
(ii)

10.00 cu.cm
(iii)

9.00 cu.cm
(iv)

8.00 cu.cm
(v)

6.00 cu.cm

Assignment Key