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# Area Aptitude Test Paper 1

1) What is the area of a triangle with base 5 meters and height 10 meters?

1. 20 square meters
2. 35 square meters
3. 25 square meters
4. 40 square meters

Explanation:

Area of a triangle = ½ * base * height
So, the area = ½* 5 * 10
=25 square meters

2) The base of a right-angled triangle is 10 and hypotenuse is 20. What is its area?

1. 52 meters
2. 58 meters
3. 68 meters
4. 60 meters

Explanation:

The area of a right angled triangle = ½ * base * height

Base = 10, Hypotenuse = 20
Height2 = Hypotenuse2 – Base2
= 202 – 162
= 400 – 256
Height2 = 144
Height = 12

Area = ½ * base * height

= ½ * 10 * 12
= 60 meters

3) The sides of a triangle are in the ratio 10: 24:26 and its perimeter is 300 m. What is its area?

1. 2500 m2
2. 3000 m2
3. 3500 m2
4. 4000 m2

Explanation:

Let the sides are 10x, 24x, and 26x.
The perimeter is 300 m.
So, 10x + 24x + 26x = 300
60x = 300
x= 5

So, the sides are 10 *5 = 50 meters
24 * 5 = 100 meters
26 * 5 = 130 meters
102 + 242 = 262 so, it is a right triangle.
100 + 576 = 676

The area of a right triangle is = 1/2 * base * height
= 1/2 * 50 * 100
= 2500 m2

4) The ratio of length and breadth of a rectangular park is 4:2. If a cat running along the boundary of the park at the speed of 18 km/hr completes one round in 10 minutes, find the area of the park in square meters.

1. 50000 sq. m.
2. 45000 sq. m.
3. 68000 sq. m.
4. 55000 sq. m.

Explanation:

One round of the park is equal to the perimeter of the park.

So, by completing one round, the cat covers a distance equal to the perimeter of the park.

Now, Distance or perimeter = speed * time
= 18 * (10/60)
= 3 km or 3000 meters

Let Length = 4x and breadth = 2x

So, Perimeter: 2 (4x + 2x) = 3000
8x + 4x = 3000
12x = 3000
x= 3000/12= 250 meters

So, Length = 4 * 250 = 1000 meters

And, Breadth = 2 * 250 = 500 meters

= 1000 * 500
= 50000 sq. m.

5) The perimeter of the rectangular field is 480 meters and the ratio between the length and breadth is 5:3. Find the area of the field.

1. 7200 m2
2. 15000 m2
3. 13500 m2
4. 54000 m2

Explanation:

Let the length of the rectangle be 5x, and breadth be 3x,
Perimeter of a rectangle = 2(l +b) = 480
2(5x + 3x) = 480
2 x 8x = 480
16x = 480
x = 480/16 = 30

∴ Length = 5 x 30 = 150 m
Breadth = 3 x 30 = 90 m

And, Area of rectangle = L x B
= 150 x 90 = 13500 m2

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