Question

Find the area of the given figure.

Answer 1

Area of the given figure = Area of two semi-circles + Area of two triangles + Area of a square
$\therefore$ Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$ [$\because$ a = 5 cm, b = 5 cm and c = 6 cm, given]
where,
$s=\frac{a+b+c}{2}=\frac{5+5+6}{2}$
$=\frac{16}{2}=8cm$

$\therefore$ Area of a triangle
$=\sqrt{8(8-5)(8-5)(8-6)}$
$=\sqrt{8\times 3\times 3\times 2}=\sqrt{144}=12c{m}^2$

$\therefore$ Area of 2 triangles $=2\times 12=24c{m}^2$

$\therefore$ Area of 2 semi-circles = Area of 1 circle

Area of a circle $=\pi r^2=\frac{22}{7}\times 3\times 3=\frac{9\times 22}{7}=\frac{198}{7}=28.28c{m}^2$

$\therefore$ Area of the square $=a^2$ $=6\times 6=36c{m}^2$ ($a$ = side of the square)

Area of the given figure
$=(24+28.28+36)c{m}^2=88.28c{m}^2$