Question

Find the area of a parallelogram given in the figure. Also, find the length of the altitude from vertex A on the side DC.

Answer 1

Area of parallelogram $ABCD=2(Areaof\Delta BCD)$

Now, the sides of a $\Delta BCD$ are:

a = 12 cm, b = 17 cm and c = 25 cm.

Semi-perimeter, $s=\frac{12+17+25}{2}=27cm$

therefore, Area of $\Delta BCD=\sqrt{s(s-a)(s-b)(s-c)}$ [by Heron’s formula]

$=\sqrt{27(27-12)(27-17)(27-25)}$

$=\sqrt{27\times 15\times 10\times 2}$

$=90c{m}^2$

Area of parallelogram $ABCD=2\times 90=180c{m}^2$

Let 'h' be the altitude of the parallelogram.

Area of parallelogram ABCD = Base × Altitude
180 = DC × h
180 = 12 × h
$h=\frac{180}{12}=15cm$
Hence, the area of parallelogram is $180c{m}^2$ and the length of altitude is 15 cm