Question

ΔABC is an equilateral triangle of side 14 cm. A semi circle on BC as diameter is drawn to meet AB at D, and AC at E. Find the area of the shaded region.

• A.
• B.
• C. 49 cm²
• D. 49sqrt(2) cm²

Answer 1

The correct option is D 49sqrt(2) cm²

O is the centre of the circle and the mid-point of BC. DO is parallel to AC. So, <DOB = 60°

Area of Δ BDO = $\frac{\sqrt{3}}{4}\times 49$= 21.22

Area of sector OBD = $\pi \times \frac{49}{6}$ = 25.66

Hence area of the shaded region

= 2[25.66 - 21.22 ]

= 8.88