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AREA PROBLEMS

Area Problems
One diagonal of a rhombus is 60% of the other diagonal. Then, area of the rhombus is how many times the square of the length of the larger diagonal?

1/5
2/5
3/10
6/7

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let one diagonal be k.Then, other diagonal = (60k/100) = 3k/5 cmArea of rhombus =(1/2) x k x (3k/5) = (3/10) = 3/10 (square of longer diagonal)Hence, area of rhombus is 3/10 times.

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

36.25%
12.25%
16.25%
56.25%

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let each side of the square be a. Then, area = . a 2 New side = 125 a 100 = 5 a 4 . New area =  5 a 4 2  =  25 a 2 16   Increase in area =  25 a 2 16 - a 2 = 9 a 2 16 Increase% =  9 a 2 16 * 1 a 2 * 100  % = 56.25%.

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

110
130
120
140

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

let length = x and breadth = y then 2(x+y) = 46 => x+y = 23 x²+y² = 17² = 289 now (x+y)² = 23² => x²+y²+2xy= 529 => 289+ 2xy = 529 => xy = 120 area = xy = 120 sq.cm

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

65%
25%
35%
75%

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

let original radius = r and  new radius = (50/100) r = r/2   original area =  ?r 2  and new area =  ? r / 2 2   decrease in area =  3 ?r 2 / 4 * 1 ?r 2  *100 = 75%

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

436
336
136
236

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

let ABCD be the given parallelogram  area of parallelogram ABCD = 2 x (area of triangle ABC)  now a = 30m, b = 14m and c = 40m  s=1/2 x (30+14+40) = 42    Area of triangle ABC =  s s - a s - b s - c      = 42 12 28 2 = 168sq m  area of parallelogram ABCD = 2 x 168 = 336 sq m

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