The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.
Mensuration
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Question

The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

KnowledgeBoat · Accepted Answer

For triangle ABC (right-angled triangle), Using the Pythagoras theorem, Base² \+ Height² = Hypotenuse² ⇒ 8² + height² = 16² ⇒ 64 + height² = 256 ⇒ height² = 256 - 64 ⇒ height² = 192 ⇒ height = ⇒ height = 8 Area of triangle ABC = x base x height = = = cm² For triangle BCD, Area of an equilateral triangle = x side² = x 8² = x 64 = 16 cm² Area of Δ ABD (shaded portion) = Area of Δ ABC - Area of Δ BDC = 32 - 16 cm² = 16 cm² Hence, the area of the shaded portion is 16 cm² = 27.712 cm².

Mathematics

The given figure shows a right-angled triangle ABC and an equilateral triangle BCD. Find the area of the shaded portion.

Mensuration

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