Question

Find the perimeter and area of the following combined figure.

Answer 1

The given combined figure is made up of a square ABCD and an equilateral triangle DEA.
Given: Side of a square $=4cm$
$\therefore$ Perimeter of the combined figure $=AB+BC+CD+DE+EA$
$=4+4+4+4+4=20cm$
$\therefore$ Perimeter of the combined figure $=20cm.$
Area of the given combined figure $=$ Area of a square + Area of an equilateral triangle
$=a^2+\frac{\sqrt{3}}{4}{a}^2\sqrt{3}=1.732$
$=4\times 4+\frac{\sqrt{3}}{4}\times 4\times 4$
$=16+1.732\times 4$
Area of the given combined figure $=16+6.928=22.928$
Area of the given figure $\simeq 22.93c{m}^2$.