Question

Find the difference in $m^2$ between the area of regular hexagonal plot each of whose side is 72 m and the area of the circular swimming pool inscribed in it. (Take $\pi =\frac{22}{7}$). [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Hexagon is made up of 6 equilateral triangles. Here, the side of triangles is 72m.

The area of each triangle is $\frac{a^2\sqrt{3}}{4}$ where a is the length of the side of the triangle.

The area of hexagon
$=6\times \frac{{72}^2\times \sqrt{3}}{4}$

$=13468.03m^2$

The radius of the circle is the height of the equilateral triangle

$=\frac{a\times \sqrt{3}}{2}=\frac{72\times \sqrt{3}}{2}=62.35$

The area of the circle is
$=\pi r^2=\pi \times {62.35}^2$

$=12217.92m^2$

Difference in area
$=13468.03-12217.92=1250.11m^2$.