Question

In the given figure, ABC is a triangle in which CDEFG is a pentagon. Triangles ADE and BFG are equilateral triangles each with side 2 cm and EF = 2 cm. Find the area of the pentagon.

(a) 8√3 cm² 

(b) 7√3 cm².

(c) 15√3 cm² 

(d) 11.28 cm²

Answer 1

(b) 7√3 cm².

AB = 6 cm, ∠C = 60º             (∴ ∠A = ∠B = 60º) 

∴ ΔABC is an equilateral triangle 

Area of ΔABC = \(\frac{\sqrt3}{4}\) × (6)² = 9√3 

Area of (ΔADE + ΔBFG) = 2 x \(\bigg(\frac{\sqrt3}{4}\times(2)^2\bigg)\) = 2√3 

∴ Area of pentagon = 9√3 - 2√3 = 7√3 cm².