Question

A field in the form of parallelogram has sides 30 m and 20 m and one of its diagonals is 40 m long. Find the area of parallelogram.

• A. $100\sqrt{15}{m}^2$
• B. $150\sqrt{15}{m}^2$
• C. $200\sqrt{15}{m}^2$
• D. $250\sqrt{15}{m}^2$

Answer 1

The correct option is B $150\sqrt{15}{m}^2$

Rough figure of the given field is shown below:


The given parallelogram-shaped field ABCD can be divided into two triangles ABC and ADC.

The area of a triangle with sides a, b and c can be calculated using Heron's formula, given by:
Area $=\sqrt{s(s-a)(s-b)(s-c)}$,
where 's' is the semi-perimeter.
[$s=\frac{a+b+c}{2}$]

$\text{For}△ABC,\text{semi-perimeter}=\frac{AB+BC+AC}{2}=\frac{30+20+40}{2}=45m$
$Area\left(\Delta ABC\right)$
$=s\sqrt{s(s-AB)(s-BC)(s-AC)}$
$=\sqrt{45(45-30)(45-20)(45-40)}$
$=\sqrt{45\times 15\times 25\times 5}$
$=\sqrt{9\times 5\times 5\times 3\times 25\times 5}$
$=75\sqrt{15}{m}^2$
Now, the other triangle also has the same dimensions.
$\therefore \text{Area of ABCD}=2\times 75\sqrt{15}=150\sqrt{15}{m}^2$