Question

Two adjacent sides of a parallelogram are 51cm and 37cm. One of its diagonals is 20cm, then its area is _____.

• A. $412c{m}^2$
• B. $512c{m}^2$
• C. $612c{m}^2$
• D. $712c{m}^2$

Answer 1

The correct option is C

$612c{m}^2$

Let ABCD be the given parallelogram as shown above.

Diagonal of a parallelogram divides it into two triangles of equal areas.

Hence, area (parallelogram ABCD) $=2\text{area}\left(\Delta BCD\right)$

Let us calculate the area of $\Delta BCD$ by using Heron’s Formula.

$s=\frac{51+37+20}{2}=\frac{108}{2}=54$

Area of $\Delta BCD$

$=\sqrt{54(54-51)(54-37)(54-20)}$

$=\sqrt{54\times 3\times 17\times 34}$

$=\sqrt{3\times 3\times 3\times 2\times 3\times 17\times 17\times 2}$

$=17\times 2\times 3\times 3=306c{m}^2$

So, area of parallelogram ABCD $=2\times 306c{m}^2=612c{m}^2$