Question

Find the area of the trapezoid in the following figure.

• A. $7$
• B. $7\sqrt{2}$
• C. $7\sqrt{3}$
• D. $\frac{7\sqrt{3}}{2}$
• E. $\frac{7\sqrt{3}}{4}$

Answer 1

The correct option is D $\frac{7\sqrt{3}}{2}$

From the figure, the triangle on the left has an angle ${60}^0$ and its adjacent side as $1$ and opp side as $h$
We know that $\tan x=\frac{opposite}{adjacent}$
$=>\tan 60=\frac{h}{1}$
$=>h=\tan 60=\sqrt{3}$
Now, area of a trapezium with parallel sides $a;b$ and perpendicular distance between them $h$ $=\frac{(a+b)h}{2}=\frac{(3+4)\sqrt{3}}{2}=\frac{7\sqrt{3}}{2}$