Area Aptitude

Area problems in aptitude tests involve calculating the space occupied within a two-dimensional boundary. These problems can include a variety of shapes such as squares, rectangles, circles, triangles, and more complex geometrical figures. Understanding how to calculate the area is essential for various real-life applications in fields like architecture, land development, and interior design.

1. Find the area of a rectangle with length 15 cm and width 10 cm.

Area of a rectangle = Length × Width = 15 cm × 10 cm = 150 cm².

2. What is the area of a square whose side is 8 cm?

Area of a square = Side × Side = 8 cm × 8 cm = 64 cm².

3. Calculate the area of a circle with radius 7 cm.

Area of a circle = π × Radius² = 3.14 × 7 cm × 7 cm ≈ 154 cm².

4. The length and breadth of a rectangle are in the ratio 3:2. If the area of the rectangle is 150 cm², find its length and breadth.

Let the length be 3x and breadth be 2x. Then, 3x × 2x = 150 cm², 6x² = 150 cm², x² = 25 cm², x = 5 cm. So, Length = 15 cm, Breadth = 10 cm.

5. Find the area of an equilateral triangle with a side of 6 cm.

Area of an equilateral triangle = (sqrt(3)/4) × Side² = (sqrt(3)/4) × 6 cm × 6 cm ≈ 15.59 cm².

6. A rectangular park 60 m long and 40 m wide is surrounded by a path of uniform width 2 m. Find the area of the path.

Area of the park = 60 m × 40 m = 2400 m².
New dimensions including path = 64 m × 44 m.
Area including path = 64 m × 44 m = 2816 m².
Area of the path = 2816 m² - 2400 m² = 416 m².

7. The radius of a circle is 14 cm. Find its area.

Area of a circle = π × Radius² = 3.14 × 14 cm × 14 cm = 616 cm².

8. A triangle has a base of 8 cm and a height of 5 cm. Find its area.

Area of a triangle = 1/2 × Base × Height = 1/2 × 8 cm × 5 cm = 20 cm².

9. Find the area of a square park whose perimeter is 64 m.

Perimeter of a square = 4 × Side.
Side = Perimeter / 4 = 64 m / 4 = 16 m.
Area of the square = Side² = 16 m × 16 m = 256 m².

10. A circle and a rectangle have the same perimeter. The diameter of the circle is 14 cm and the length and breadth of the rectangle are in the ratio 3:2. Find the area of the rectangle.

Perimeter of the circle = π × Diameter = 3.14 × 14 cm = 44 cm (approx).
Let length = 3x and breadth = 2x.
Perimeter of the rectangle = 2(Length + Breadth) = 2(3x + 2x) = 10x.
10x = 44 cm, x = 4.4 cm.
Area of the rectangle = Length × Breadth = 3x × 2x = 3 × 4.4 cm × 2 × 4.4 cm = 168 cm².

11. The diagonal of a rectangle is 17 cm long and its breadth is 8 cm. Find the area of the rectangle.

Using Pythagoras theorem, length = sqrt(Diagonal² - Breadth²) = sqrt(17² - 8²) = 15 cm.
Area of rectangle = Length × Breadth = 15 cm × 8 cm = 120 cm².

12. What is the area of a parallelogram with base 10 cm and height 5 cm?

Area of a parallelogram = Base × Height = 10 cm × 5 cm = 50 cm².

13. A rhombus has a side of 10 cm and one of its diagonals is 16 cm. Find its area.

Other diagonal = sqrt(4 × Side² - Diagonal²) = sqrt(4 × 10² - 16²) = 12 cm.
Area of rhombus = 1/2 × Product of diagonals = 1/2 × 16 cm × 12 cm = 96 cm².

14. The area of a trapezium is 384 cm² and the length of one of the parallel sides is 16 cm and the height is 8 cm. Find the length of the other parallel side.

Area of a trapezium = 1/2 × (Sum of parallel sides) × Height.
384 cm² = 1/2 × (16 cm + other side) × 8 cm.
Other side = 32 cm.

15. The length of a rectangle exceeds its breadth by 4 cm. If the length is decreased by 3 cm and the breadth is increased by 2 cm, the area of the new rectangle is 54 cm². Find the area of the original rectangle.

Let the breadth be x cm. Then, length = x + 4 cm.
New length = x + 1 cm, New breadth = x + 2 cm.
(x + 1)(x + 2) = 54 cm², x² + 3x - 52 = 0.
Original length = x + 4 cm, Original breadth = x cm.
Area = x(x + 4) cm². Solve for x and find the area.

16. A circular park of radius 20 m is surrounded by a circular path of width 4 m. Find the area of the path.

Outer radius of the path = 20 m + 4 m = 24 m.
Area of the larger circle = π × (24 m)².
Area of the park = π × (20 m)².
Area of the path = Area of the larger circle - Area of the park = π × [(24 m)² - (20 m)²] ≈ 1256 m².

17. The sides of a triangle are in the ratio 3:4:5 and its perimeter is 60 cm. Find the area of the triangle.

Let the sides be 3x, 4x, and 5x. Then, 3x + 4x + 5x = 60 cm, x = 5 cm.
Sides are 15 cm, 20 cm, and 25 cm. 
Using Heron's formula, area = sqrt(s × (s - a) × (s - b) × (s - c)), where s is the semi-perimeter.
s = 30 cm, area = sqrt(30 × 15 × 10 × 5) cm² ≈ 72 cm².

18. A rectangular plot 70 m long and 50 m wide is to be covered with grass, leaving an area of 2100 m² uncovered. Find the width of the border left uncovered.

Let the width of the border be x m.
Area of the plot = 70 m × 50 m.
Area of the covered portion = (70 - 2x) m × (50 - 2x) m.
(70 - 2x) × (50 - 2x) = 3500 m² - 2100 m², x = 3 m.

19. The diagonals of a rhombus are 16 cm and 12 cm. Find its area.

Area of a rhombus = 1/2 × Product of its diagonals = 1/2 × 16 cm × 12 cm = 96 cm².

20. A wire is bent in the form of a square with area 121 cm². If the same wire is bent into a circle, find the area of the circle.

Side of the square = sqrt(121) cm = 11 cm.
Perimeter of the square = 4 × 11 cm = 44 cm.
Circumference of the circle = Perimeter of the square = 44 cm.
Radius of the circle = Circumference / (2π) = 44 / (2 × 3.14) cm ≈ 7 cm.
Area of the circle = π × Radius² ≈ 3.14 × 7 cm × 7 cm ≈ 154 cm².