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.

• A. $150{\text{cm}}^2,10\text{cm}$
• B. $150{\text{cm}}^2,15\text{cm}$
• C. $180{\text{cm}}^2,10\text{cm}$
• D. $180{\text{cm}}^2,15\text{cm}$

Answer 1

The correct option is D $180{\text{cm}}^2,15\text{cm}$

Area of parallelogram ABCD = 2(Area of $\Delta BCD$)
Now, the sides of a $\Delta BCD$ are:
a = 12 cm, b = 17 cm and c = 25 cm.
Semi-perimeter , $s=\frac{12+17+25}{2}=\frac{54}{2}=27\text{cm}$
$\therefore \text{Area of}\Delta BCD=\sqrt{s(s-a)(s-b)(s-c)}$ [by Heron’s formula]
$=\sqrt{27(27-12)(27-17)(27-25)}$
$=\sqrt{27\times 15\times 10\times 2}$
$=\sqrt{9\times 3\times 3\times 5\times 5\times 2\times 2}$
$=3\times 3\times 5\times 2=90{\text{cm}}^2$

Area of parallelogram ABCD = 2 $\times$ 90 = 180 cm${}^2$
Let 'h' be the altitude of the parallelogram.
Area of parallelogram ABCD = Base $\times$ Altitude
$\Rightarrow 180=DC\times h$
$\Rightarrow 180=12\times h$
$\therefore h=\frac{180}{12}=15\text{cm}$
Hence, the area of parallelogram is 180 cm${}^2$ and the length of altitude is 15 cm.