In the given figure, △ABC is an equilateral triangle having each side equal to 10 cm and △PBC is right angled at P in which PB = 8 cm. Find the area of the shaded region.
Mensuration
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Question

In the given figure, △ABC is an equilateral triangle having each side equal to 10 cm and △PBC is right angled at P in which PB = 8 cm. Find the area of the shaded region.

KnowledgeBoat · Accepted Answer

Given, △ABC is an equilateral triangle. Each side = 10 cm By formula, Given, PB = 8 cm and BC = 10 cm By using the Pythagoras theorem in △PBC, ⇒ BC2 = PB2 + PC2 ⇒ 102 = 82 + PC2 ⇒ 100 = 64 + PC2 ⇒ PC2 = 36 ⇒ PC = ⇒ PC = 6 cm. Area of triangle = × base × height Area of △PBC = × PB × PC = × 8 × 6 = 4 × 6 = 24 cm2. Shaded region = Area of △ABC − Area of △PBC = 43.3 - 24 = 19.3 cm2. Hence, area of shaded region = 19.3 cm2.

Mathematics

In the given figure, △ABC is an equilateral triangle having each side equal to 10 cm and △PBC is right angled at P in which PB = 8 cm. Find the area of the shaded region.

Mensuration

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Mathematics

In the given figure, △ABC is an equilateral triangle having each side equal to 10 cm and △PBC is right angled at P in which PB = 8 cm. Find the area of the shaded region.

Mensuration

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