Question

What is the area of an equilateral triangle whose side is 8cm?Also find the corresponding altitude of the base. [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Perimeter of the triangle will be = 8 + 8 + 8 = 24 cm

S = $\frac{Perimeter}{2}$ = $\frac{(a+b+c)}{2}$ = $\frac{24}{2}$ =12 cm

Area = $\sqrt{s(s-a)(s-b)(s-c)}$
Area = $\sqrt{12(12-8)(12-8)(12-8)}$ =16$\sqrt{3}c{m}^2$

Now Area of triangle = ($\frac{1}{2}$) × base ×height $\Rightarrow$ 16$\sqrt{3}$ = ($\frac{1}{2}$) × 8 × height

Therefore Height = 4$\sqrt{3}cm$