Question

A park, in the shape of a quadrilateraI $ABCD$, has $\angle C={90}^{\circ },AB=9$ m, $BC=12$ m, $CD=5$ m and $AD=8$ m. How much area does $△BCD$ occupy?

• A. $30m^2$
• B. $13m^2$
• C. $169m^2$
• D. $12m^2$

Answer 1

The correct option is A $30m^2$

Given, a quadrilateral $ABCD$ in which $AB=9$ m, $BC=12$ m, $CD=5$ m and $AD=8$ m.

We divide the quadrilateral in two triangular region $ABD$ and $BCD$.

Now, In $△BCD$, $\angle C={90}^{\circ }$.

$\therefore$ Area of $△BCD=\frac{1}{2}\times$ base $\times$ height

$\Rightarrow \frac{1}{2}\times 5\times 12=30m^2$