Question

Question 82

Find the area of shaded portion.

Answer 1

Area of shaded portion=Area of trapezium ABCH+Area of trapezium CDEF + Area of rectangle GHCF

Area of trapezium = $\frac{1}{2}\times \text{(Sum of parallel sides)}\times \text{(Height)}$

$\therefore \text{Area of trapezium ABCH}$
$=\frac{1}{2}\times \left(\right[12-3]+6)\times 4$
$=\frac{1}{2}\times 9\times 4$
$=9\times 2$
$=18c{m}^2$

$\therefore \text{Area of trapezium CDEF}$
$=\frac{1}{2}\times (8+[16-4\left]\right)\times 3$
$=\frac{1}{2}\times (8+12)\times 3$
$=\frac{1}{2}\times 20\times 3$
$=10\times 3$
$=30c{m}^2$

$\therefore \text{Area of rectangle GHCF}$
$=4\times 3$
$=12c{m}^2$

$\text{Hence, area of shaded portion}$
$=(18+30+12)c{m}^2$
$=60c{m}^2$