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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.

9 cm
3?3 cm
3 cm
?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
A railing of 288 m is required for fencing a semi-circular park. Find the area of the park. (? = 22/7)

4928 m2
9856 m2
8956 m2
9865 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 radius of a circle is so increased that its circumference increased by 5%. The area of the circle, then increases by

10.5 %
10.25%
11.25%
12.5%

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Increase in circumference of circle = 5%? Increase in radius is also 5%.Now, increase in area of circle = 2a + (a2/100) %Where, a = increase in radius= 2 x 5 + (5 x 5)/100 % = 10.25%

Area Problems
If the side of a square is increased by 25%, then how much percent does its area get increased?

50
56.25
156.25
125

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let area 100 m2Then, side = 10 m New side = 125 % of 10= (125/100) x 10= 12.5 m New area = 12.5 x 12.5 m2=(12.5)2 sq. m? Increase in area = (12.5)2 - (10)2 m2= 22.5 x 2.5 m2=56.25 m2% Increase = 56.25 %

Area Problems
The breadth of a rectangle is 25 m. The total cost of putting a grass bed on this field was ? 12375, at the rate of ? 15 per sq m. What is the length of the rectangular field?

32 m
33 m
30 m
27 m

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Area to the rectangular field = 12375/15 = 825 sq mAccording to the question, (L x B) = 825 [L = length and B = breadth]? L x 25 = 825 ? L = 825/25 = 33 m

Area Problems
In a triangle ABC, BC = 5 cm AC = 12 cm and AB = 13 cm. The length of a altitude drawn from B on AC is?

6 cm
4 cm
7 cm
5 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

? s= (13 + 5 + 12) / 2 cm = 15cms-a = 2 cm, s-b = 10 cm and s-c = 3 cm ? Area = ? (15 x 2 x 10 x 3 ) cm2= 30 cm2? (12 x h) / 2 = 30 ? h = 5 cm

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