**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?

- 32 %
- 42 %
- 35 %
- 45 %

**Answer:** A

**Explanation:**

Let original length = X

Original breadth = Y

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?

- 3600 m
^{2} - 2600 m
^{2} - 3000 m
^{2} - 2000 m
^{2}

**Answer:** B

**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 m^{2}

28) The side of a rhombus is 25 m, and one of its diagonal is 30 meters. What is its area?

- 400 sq. m.
- 450 sq. m.
- 500 sq. m.
- 600 sq. m.

**Answer:** D

**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: 15^{2} + X^{2} = 25^{2}

225 + X^{2} = 625

X^{2} = 625 – 225

X^{2} = 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?

- 8 meters
- 7 meters
- 9 meters
- 10 meters

**Answer:** C

**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.

2X^{2} = 162

X^{2} = 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?

- 3.3 meters
- 4.5 meters
- 5.3 meters
- 6.5 meters

**Answer:** A

**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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