Question

Calculate the area of the figure shown above, which is not drawn to scale.

• A. $630c{m}^2$
• B. $620c{m}^2$
• C. $640c{m}^2$
• D. $600c{m}^2$

Answer 1

Answer: (A)

$630c{m}^2$

Given, $AB=15cm,BC=26cm,EC=25cm,DF=12cm$
Let $BG\perp EC$
$\therefore EG=AB=15cm$
$\therefore GC=EC-EG$
$=(25-15)$
$=10cm$
In $△BGC,\angle BGC={90}^{\circ }$
$B{G}^2=B{C}^2-G{C}^2$
$={26}^2-{10}^2$
$=676-100$
$=576$
$\therefore BG=24cm$
$\therefore AE=BG=24cm$

Now, the area of the given figure $=$ Area of the trapezium $ABCE+$ Area of the $△ECD$
$=\frac{1}{2}\times \text{parallel sides}\times \text{height}+\frac{1}{2}\times \text{base}\times \text{height}$
$=\frac{1}{2}\times (AB+EC)\times AE+\frac{1}{2}\times EC\times DF$
$=\frac{1}{2}\times (15+25)\times 24+\frac{1}{2}\times 25\times 12$
$=\frac{1}{2}\times 40\times 24+25\times 6$
$=20\times 24+25\times 6$

$=480+150$

$=630c{m}^2$

Hence, the area of the given figure is $630c{m}^2$.