ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AB = 20 cm, find the area of the shaded portion. [Take √3 = 1.73]

Given: AB = 20 cm (ABC is an equilateral triangle)

D is the midpoint of BC ⇒ BD = DC

Thus, BD = 10 cm

BDE is also equilateral ⇒ side = BD = 10 cm

Area of equilateral triangle = $\dfrac{\sqrt{3}}{4}$ x side²

Area of shaded portion = Area of triangle ABC - Area of triangle BDE

$= \dfrac{\sqrt{3}}{4} \times AB^2 - \dfrac{\sqrt{3}}{4} \times BD^2\\[1em] = \dfrac{\sqrt{3}}{4} \times 20^2 - \dfrac{\sqrt{3}}{4} \times 10^2\\[1em] = 400\dfrac{\sqrt{3}}{4} - 100\dfrac{\sqrt{3}}{4} \\[1em] = \dfrac{\sqrt{3}}{4}(400 - 100) \\[1em] = \dfrac{300\sqrt{3}}{4} \\[1em] = \dfrac{300 \times 1.73}{4} \\[1em] = \dfrac{519}{4} \\[1em] = 129.75$

Hence, the area of the shaded portion = 129.75 cm².