# 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?

1. 32 %
2. 42 %
3. 35 %
4. 45 %

Explanation:

Let original length = X

So, original area = XY
So, decrease in area = X*Y -  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?

1. 3600 m2
2. 2600 m2
3. 3000 m2
4. 2000 m2

Explanation:

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?

1. 400 sq. m.
2. 450 sq. m.
3. 500 sq. m.
4. 600 sq. m.

Explanation:

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?

1. 8 meters
2. 7 meters
3. 9 meters
4. 10 meters

Explanation:

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?

1. 3.3 meters
2. 4.5 meters
3. 5.3 meters
4. 6.5 meters

Explanation:

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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