Area Aptitude Test Paper 6
26) A blanket, when bleached, decreases in length by 20% and in breadth by 15%. What is the percentage decrease in its area?
Let original length = X
Original breadth = Y
So, original area = XY
27) The difference between the length and breadth of a rectangle is 25 meters. If the perimeter of this rectangle is 210 meters, what is its area?
The perimeter: 2 (L + B) = 210 or L+ B = 105 ...... (i)
As per the question: (L - B) = 25 ....... (ii)
Solving the above two equations:
L + B = 105
B = 105 - L
Put the value of B in (ii).
L - (105 - L) = 25
L - 105 + L = 25
2L = 25 + 105
2L = 130
L = 65
So, - B = 105 - 65 = 40
Now, area of a rectangle: L *B= 65 * 40 = 2600 m2
28) The side of a rhombus is 25 m, and one of its diagonal is 30 meters. What is its area?
Diagonal of a rhombus bisect and divide each other equally.
So, half of the given diagonal = 15 m.
Let the half of the other diagonal = X
So, as per the Pythagoras theorem: 152 + X2 = 252
225 + X2 = 625
X2 = 625 - 225
X2 = 400
X = 20
So, the length of the other diagonal is double of X: 20 + 20 = 40 m.
Now, Area of a rhombus = 1/2 * (product of diagonals)= 1/2 * 30 * 40
= 600 sq. m.
29) The area of a parallelogram is 162 square meters. If its altitude is twice the corresponding base, find the length of the base?
Area of a parallelogram = (Base * Height)
Let the length of the base is = X
Then, the altitude or height is = 2X
So, Area: X * 2X = 162 sq. m.
2X2 = 162
X2 = 81
X = 9 meters (length of the base).
30) The area of a trapezium is 1500 sq. m. If the parallel sides are in the ratio of 12: 18 and the distance between the parallel sides is 32 meters, what is the length of the smaller parallel side?
Trapezium is a quadrilateral with one pair of parallel sides.
Let the length of the smaller side = 12x
Length of the bigger parallel side = 18x
Distance between parallel sides = 32 meters
Area of a trapezium = 1/2 * (sum of parallel sides) * distance between them.
So, as per the question: 1500 = 1/2 (12x +18x) * 30
1500 = 1/2 * 30x * 30
1500 = 30x * 15
30x = 1500 /15
30x = 100
x= 100 /30 = 3.3 meters
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