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Area Problems

Area Problems
The area of an equilateral triangle is ? 243 /4 sq cm. Find the length of its side.

?3 cm
3 cm
9 cm
3?3 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

According to the question,area = ?3a2/4 = ?243 /4? a2 = ?81 x 3/?3 ? a = ?9 = 3 cm

Area Problems
The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

20 cm
18 cm
41 cm
9 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

√l2 + b2 = √41. Also, lb = 20. (l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81 ⟹ (l + b) = 9. ∴ Perimeter = 2(l + b) = 18 cm

Area Problems
A circular disc of area 0.49 ? square meters, rolls down a length of 1.76 km. The number of revolutions it makes is?

4000
600
300
400

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Area = ?r2 = 0.49? ? r = 0.7 mNumber of revolutions = total distance / circumference = (1.76 x 1000) / (2 x 22/7 x 0.7) = 400

Area Problems
The area of a circle is increased by 22 sq cm when its radius is increased by 1 cm. Find the original radius of the circle.

6 cm
3.5 cm
3.2 cm
3 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let original radius be r.Then, according to the questions,? (r + 1)2 - ?r2 = 22? ? x [(r + 1)2 - r2] = 22? (22/7) x (r + 1 + r ) x (r + 1 - r) = 22? 2r + 1 = 7 ? 2r = 6 ? r = 6/2 = 3 cm

Area Problems
The length of a rectangular field is increased by 60 % . By what percent would the width have to be decreased to maintain the same area?

371/2%
120%
60%
75%

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let length = L and breadth = BLet , New breadth = ZThen, New length = ( 160 / 100) L.= 8L / 5? 8L / 5 x Z = LBor Z = 5B/8Decrease in breadth = (B-5B/8)= 3B/8? Decrease in percent = (3B/8 x1/B ) x 100 %= 371/2%

Area Problems
The area of a rectangle, 144 m long is the same as that of a square having a side 84 m long. The width of the rectangle is?

Cannot be determined
49 m
14 m
7 m

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Area of the square = (84 + 84) m2Area of the rectangle = (144 x width) m2From question both area would be same,? Width = (84 x 84) / 144 m = 49 m

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