Area of trapezium $= \frac{1}{2} \times (a + b) \times h = \frac{1}{2} \times (10 + 12) \times 5 = \frac{1}{2} \times 22 \times 5 = 55\text{ cm}^2$.

Area of a rhombus $= \frac{1}{2} \times d1 \times d2 = \frac{1}{2} \times 10 \times 8.2 = 41\text{ cm}^2$.

Lateral Surface Area of cuboid $= 2 \times \text{height} \times (\text{length} + \text{breadth}) = 2h(l + b)$.

Volume of a cylinder $= \text{Base area} \times \text{height} = \pi r^2 h$.

Question 1

The parallel sides of a trapezium are $10	ext{ cm}$ and $12	ext{ cm}$, and its height is $5	ext{ cm}$. Find its area.

Accepted Answer

Area of trapezium $= \frac{1}{2} 	imes (a + b) 	imes h = \frac{1}{2} 	imes (10 + 12) 	imes 5 = \frac{1}{2} 	imes 22 	imes 5 = 55	ext{ cm}^2$.

Question 2

Find the area of a rhombus whose diagonals are of lengths $10	ext{ cm}$ and $8.2	ext{ cm}$.

Accepted Answer

Area of a rhombus $= \frac{1}{2} 	imes d1 	imes d2 = \frac{1}{2} 	imes 10 	imes 8.2 = 41	ext{ cm}^2$.

Question 3

What is the total surface area of a cube of side $a$?

Accepted Answer

A cube has 6 square faces, each of area $a^2$. Therefore, the total surface area $= 6a^2$.

Question 4

The lateral surface area of a cuboid with length $l$, breadth $b$, and height $h$ is given by:

Accepted Answer

Lateral Surface Area of cuboid $= 2 	imes 	ext{height} 	imes (	ext{length} + 	ext{breadth}) = 2h(l + b)$.

Question 5

The formula for the volume of a cylinder with base radius $r$ and height $h$ is:

Accepted Answer

Volume of a cylinder $= 	ext{Base area} 	imes 	ext{height} = \pi r^2 h$.

Mensuration