Question

The trapeziums making up the roofing sheet are all of equal area. If the height of one trapezium is 5 m and the sum of their parallel sides is 44 m, find the total area of the roofing sheet in the picture given below.

• A. $1320m^2$
• B. $1230m^2$
• C. $1330m^2$
• D. $660m^2$

Answer 1

The correct option is A $1320m^2$


In the picture seen above, we see that the entire roofing sheet is made up of 12 equal sized trapeziums.
Given: Height of one trapezium = 5 m
Sum of their parallel sides = 44 m
Area of a trapezium $=\frac{1}{2}\text{height}\times \text{(sum of their parallel sides)}$
$\therefore$ Area of 1 trapezium in the roofing sheet $=\frac{1}{2}\times \left(5\right)\times \left(44\right)=110m^2$
The roofing sheet has 12 such trapeziums.
Hence, the total area of the roofing sheet $=12\times 11=1320m^2$