Question

The area of the trapezium REMN, in the above given figure is ______.

• A. $42.5c{m}^2$
• B. $45.2c{m}^2$
• C. $42c{m}^2$
• D. $42.2c{m}^2$

Answer 1

The correct option is A $42.5c{m}^2$

Area of trapezium = $\frac{1}{2}\left(sumofparallelsides\right)\times height$

The above trapezium is split into a square and 2 right triangles.
The side of the square = 5 cm, which is also the height of the trapezium.
Hence, height of trapezium = 5 cm
Length of 1 parallel side = 5 cm
Length of the other parallel side = Base of both the triangles + side of the square = (3+4) +5 = 12 cm
Hence, sum of the parallel sides of the trapezium, REMN = 5 + 12 = 17 cm
$\therefore \text{Area of the trapezium}=\frac{1}{2}(5+12)\times 5$

$=42.5c{m}^2$