Question

Find the area of the the figure given above.

Answer 1

The given figure is a composite shape composed of 4 acute triangles and 1 rectangle.


Thus, the area of the given figure is the sum of the areas of its components.

We know:

• $\text{Area of a triangle}=\frac{1}{2}\times \text{Base}\times \text{Height}$
• $\text{Area of a rectangle}=\text{Length}\times \text{Width}$

$\therefore$ Area of $\Delta ABC$
$=\frac{1}{2}\times BC\times AU$
$=\frac{1}{2}\times QL\times 6(\because BC=QL)$
$=\frac{1}{2}\times 10\times 6$
$=30\text{sq units}$

Similarly, $\text{Area of}\Delta QRL=30\text{sq units}$

Area of $\Delta CPQ$
$=\frac{1}{2}\times CQ\times PV$
$=\frac{1}{2}\times BL\times 3(\because CQ=BL)$
$=\frac{1}{2}\times 5\times 3$
$=\frac{15}{2}$
$=7.5\text{sq units}$

$\text{Similarly, Area of}\Delta BHL=7.5\text{sq units}$

Area of rectangle CBLQ
$=QL\times BL$
$=10\times 5$
$=50\text{sq units}$

Area of the entire figure
$=\text{Area of}\Delta ABC+\text{Area of}\Delta CPQ+\text{Area of}\Delta QRL+\text{Area of}\Delta BHL+\text{Area of}CBLQ$
$=30+7.5+30+7.5+50$
$=125\text{sq units}$