# Area Questions

Q:

If each side of a square is increased by 25%, find the percentage change in its area?

 A) 65.25 B) 56.25 C) 65 D) 56

Explanation:

let each side of the square be a , then area = a x a

As given that The side is increased by 25%, then

New side = $\inline \fn_jvn \small \frac{125a}{100}$ = $\inline \fn_jvn \small \frac{5a}{4}$

New area = $\inline \fn_jvn \small \left ( \frac{5a}{4} \right )^{2}$

increased area= $\inline \fn_jvn \small \frac{25a^{2}}{16}-a^{2}$

Increase %= $\inline \fn_jvn \small \frac{\left [ \frac{9a^{2}}{16} \right ]}{a^{2}}x100$ % = 56.25%

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Q:

If the radius of a circle is decreased by 50%, find the percentage decrease in its area.

 A) 55% B) 65% C) 75% D) 85%

Explanation:

New radius = $\inline \fn_cm \frac{50}{100}R$$\inline \fn_cm \frac{R}{2}$

Original area =$\inline \fn_cm \tiny \prod R^{2}$  and new area = $\inline \fn_cm \tiny \prod(\frac{R}{2})^{2}=\frac{\prod R^{2}}{4}$

Decrease in area = $\inline \fn_cm \tiny \frac{3\prod R^{2}}{4}\times \frac{1}{\prod R^{2}}\times 100$ = 75%

40 15514
Q:

A man walked diagonally across a square lot. Approximately, what was the percent saved by not walking along the edges?

 A) 30 B) 40 C) 50 D) 60

Explanation:

Let the side of the square(ABCD) be x meters.

Then, AB + BC = 2x metres.

AC = $\inline \fn_jvn \sqrt{2}x$ = (1.41x) m.

Saving on 2x metres = (0.59x) m.

Saving % =$\inline \fn_jvn \frac{0.59x}{2x}\times 100$ = 30% (approx)

24 13567
Q:

A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is

 A) 136 B) 236 C) 336 D) 436

Explanation:

let ABCD be the given parallelogram

area of parallelogram ABCD = 2 x (area of triangle ABC)

now a = 30m, b = 14m and c = 40m

$\inline \fn_jvn s=\frac{1}{2}\times \left ( 30+14+40 \right ) = 42$

Area of triangle ABC = $\inline&space;{\color{Black}\sqrt{s(s-a)(s-b)(s-c)}}$

= $\inline&space;{\color{Black}\sqrt{42(12)(28)(2)}}$= 168sq m

area of parallelogram ABCD = 2 x 168 = 336 sq m

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Q:

If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle.

 A) 110 B) 120 C) 130 D) 140

Explanation:

let length = x and breadth = y then

2(x+y) = 46  $\inline \fn_cm \Rightarrow$  x+y = 23

x²+y² = 17² = 289

now (x+y)² = 23²

$\inline \fn_cm \Rightarrow$x²+y²+2xy= 529

289+ 2xy = 529

$\inline \fn_cm \Rightarrow$ xy = 120

area = xy = 120 sq.cm