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Area Problems

Area Problems
The length of each side of an equilateral triangle having an area of 4?3 cm 2 is?

?3/4 cm
3 cm
4/?3 cm
4 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Area of equilateral triangle = ?3/4 a2 = 4?3.? a2 = 16? a = 4 cm

Area Problems
A rectangular plot is half as long again as it broad. The area of the lawn is 2/3 hectares. The length of the plot is?

33 meters
66.66 meters
(100/ ? 3 ) meters
100 meters

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let breadth = b meters. then, length = 3b/2 meters ? b x 3b/2 = 2/3 X 10000? b2 = (4 x 10000)/9? b = ( 2 X 100)/3 m ? Length = (3/2) x (2/3) x 100 m= 100 m

Area Problems
A circular road runs rounds a circular ground. If the difference between the circumference of the outer circle and the inner circle is 66 meters, the width of the road is?

7 meters
10.5 meters
5.25 meters
21 meters

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let outer radius be R and inner radius be r.Then from question 2?R - 2?r = 66? 2? (R-r) = 66? (2 x 22)/7 x (R - r) = 66? (R-r) = (66 x 7) / 44= 10.5 m

Area Problems
The length and breadth of a square are increased by 40% and 30% respectively. The area of a resulting rectangle exceeds the area of the square by?

82%
None of these
42%
62%

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let the side of the square = 100 m So area of square = 100 x 100 = 10000.New length = 140 m, New breadth = 130 mIncrease in area = [(140 x 130) - (100 x 100)] m2= 8200 m2? Required increase percent = (8200/ 10000) x 100 % = 82%

Area Problems
A railing of 288 m is required for fencing a semi-circular park. Find the area of the park. (? = 22/7)

8956 m2
9856 m2
9865 m2
4928 m2

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let the radius of the park be r, then?r + 2r = 288(? + 2)r = 288? [(22/7) + 2]r = 288? r = (288 x 7)/36 = 56 ? Area of the park = (1/2)?r2= (1/2) x (22/7) x 56 x 56= 4928

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

41 cm
9 cm
18 cm
20 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

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