Area of the Polygons

Solved Questions on Area of Polygons

1. Find the area of a regular hexagon with a perimeter of 36 cm.

a) 93.53 cm²
b) 98.23 cm²
c) 86.28 cm²
d) 66.66 cm²

Answer: a) 93.53 cm² 

Explanation: Since a hexagon has six sides, the length of each side is 36 cm / 6 = 6 cm.
Using the formula for the area of a regular polygon, we have: A = (3√3 / 2) x a²
= (3√3 / 2) x 6²
= (3√3 / 2) x 36
= 93.53 cm²

2. A rhombus has diagonals of lengths 6 cm and 8 cm. What is the area of the rhombus?

a) 12 cm²
b) 24 cm²
c) 30 cm²
d) 48 cm²

Answer: b)

Explanation: The area of a rhombus = (d₁ x d₂) / 2
where d₁ and d₂ are the lengths of the diagonals.
Plugging in the given values, we get:
Area = (6 x 8) / 2
Area = 24 cm²

Therefore, the answer is (b) 24 cm².

3. Find the area of the figure given below:

a) 5 cm²
b) 6 cm²
c) 7 cm²
d) 8 cm²

Answer: a) 5 cm²

Explanation: Split the above diagram into two rectangles
Area of a rectangle ABDC = 3 × 1 = 3 cm²
Area of a rectangle EFGD = 2 × 1 = 2 cm²

Therefore, Total Area = Area of a rectangle ABDC + Area of a rectangle EFGD
= 3 + 2 cm² = 5 cm²

Area of the given figure = 5 cm²

4. A parallelogram has a base of 6 cm and a height of 8 cm. What is the area of the parallelogram?

a) 12 cm²
b) 24 cm²
c) 32 cm²
d) 48 cm²

Answer: d)  48 cm²

Explanation: The formula for the area of a parallelogram is base times height. Using the given values, we have:
Area = 6 cm × 8 cm = 48 cm²

5. A rectangular garden measures 10 m by 15 m. What is the area of the garden?

a. 100 m²
b. 150 m²
c. 200 m²
d. 250 m²

Answer: b) 150 m²

Explanation: Area = 10 m x 15 m = 150 m²
Therefore, the area of the garden is 150 m².

Practice Questions on Area of Polygon

1. A rhombus has diagonals of lengths 10 cm and 12 cm. What is the area of the rhombus?

a) 60 cm²
b) 120 cm²
c) 144 cm²
d) 240 cm²

Answer: a) 60 cm²

2. A triangle has a base of 8 cm and a height of 12 cm. What is the area of the triangle in cm²?

a) 32 cm²
b) 36 cm²
c) 48 cm²
d) 52 cm²

Answer: c) 48 cm²

3. A trapezium has a height of 6 m, a top base of 8 m, and a bottom base of 12 m. What is the area of the trapezium in m²?

a) 40 m²
b) 52 m²
c) 58 m²
d) 60 m²

Answer: d) 60 m²

4. Find the area of an equilateral triangle in cm² with a side length 4 cm.

a) 4√3
b) 5√2
c) 7√3
d) 12√3

Answer: a) 4√3

5. A regular hexagon has a side length of 6 m. What is the area of the hexagon?

a) 24√3 m²
b) 72√3 m²
c) 60√3 m²
d) 54√3 m²

Answer: d) 54√3 m²

6. A square has an area of 144 square feet. What is the length of each side of the square?

a) 12 feet
b) 16 feet
c) 18 feet
d) 24 feet

Answer: a) 12 feet

7. The side of an equilateral triangle of area 64√3 cm² is:

a) 12 cm
b) 14 cm
c) 16 cm
d) 18 cm

Answer: c) 16 cm

8. Find the area of the figure given below:

a) 200 cm²
b) 400 cm²
c) 600 cm²
d) 800 cm²

Answer: b) 400 cm²

9. Find the area of the figure given below:

a) 156 cm²
b) 132 cm²
c) 122 cm²
d) 100 cm²

Answer: c) 122 cm²

10. If the area of a parallelogram is 24 cm² and its height is 4 cm, what is the length of its base?

a) 2 cm
b) 4 cm
c) 6 cm
d) 8 cm

Answer: c) 6 cm