Area and Perimeter - Aptitude Questions and Answers Part 2

6. Trees are grown along the border of a semi-circular piece of land which is a stretch of 324 m. Find the area of the land.

a. 18 sq. m.
b. 5248 sq. m.
c. 5368 sq. m.
d. 6237 sq. m.

Answer: d. 6237 sq.m.

Explanation:


Border of the semi-circular piece of land means perimeter of the garden.
Perimeter of a semi-circle = πr + 2r
∴ πr + 2r = 324
∴ r(π+2) = 324

∴ r (22+ 2) = 324
7
∴ r (36) = 324
7
∴ r = 63m
Area of semi-circle garden =1πr2 =1 x 22x 63 x 63 = 6237 sq.m.
22 x 7


7. Ratan takes turns to cycle around the circular garden and through the diameter of the garden on alternate days. His speed each day is 6m/min but when he cycles through the diameter, he takes 1 hr less to cross the park. Find the diameter of the park.

a. 1530 m
b. 1680 m
c. 1750 m
d. 3600 m

Answer: b. 1680 m

Explanation:

We know that, Time =Distance
Speed
Speed = 60m/min =60m/sec = 1 m/sec
60
We know that,
Time along the park (circumference) - Time along the diameter = 60 minutes
∴2πr-2r= 60 minutes
11
∴ 2r (22- 1) = 3600 seconds
7
∴ r = 840m
∴ Diameter = 2 x radius = 1680m


8. Find the total area covered by the triangles in the figure given below.



a. 432 sq.cm.
b. 122 sq.cm.
c. 72 sq.cm.
d. 192 sq.cm.

Answer: a. 432 sq.cm.

Explanation:

Diameter = 8cm; So, radius = 4cm
Inscribing triangle in semicircle means having all vertices of triangles touch or lie on the border of the semicircle.

Area of triangles = 3 x area of equilateral triangle = 3 x3(side)2
4
∴ Area = 3 x3(4)2 = 123 = 144 x 3 = 432 sq.cm.
4


9. A rectangle and a circle have same area. There is a difference of 12 cm in the length and breadth of the rectangle and its perimeter is 200 cm. Find the radius of the circle.

a. 14πcm
b. 22cm
c. 25cm
d. 28cm

Answer: d. 28cm

Explanation:

Length = L and breadth = B
Perimeter = 200 = 2(Length + Breadth)
∴ 200 = 2(L + L - 12)
∴ L = 56cm
∴ B = L - 12 = 44cm
Area of rectangle = L x B = 56 x 44 = Area of circle

∴ 56 x 44 = πr2 =22r2
7
∴ r2 =56 x 44 x 7= 784
22
∴ r = 28cm


10. The area of a square piece of fabric is same as the area of a circular piece of fabric with diameter 8 cm. Find the perimeter of the square.

a. 4π
b. 4π
c. 16π
d. 32

Answer: c. 16π

Explanation:

We know,
Area of circle = Area of Square
∴ πr2 = (side)2

∴ side = π x r = π xdiameter= 4π
2
∴ Perimeter of square = 4 x side = 16π

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