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Standard X

Mathematics

Area of a Sector of a Circle

In the given ...

Question

In the given figure, radius of circle is 3.4 cm and perimeter of sector P-ABC is 12.8 cm . Find A(P-ABC).

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Solution

Radius of the circle, r = 3.4 cm

Perimeter of sector P-ABC = 12.8 cm

Let l be the length of the arc ABC.

∴ l + 2r = 12.8 cm

⇒ l + 2 × 3.4 = 12.8

⇒ l = 12.8 − 6.8 = 6 cm

∴ A(P-ABC) = Area of the sector PABC = $\frac{1}{2} l r = \frac{1}{2} \times 6 \times 3.4$ = 10.2 cm²

Thus, A(P-ABC) is 10.2 cm².

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In the given figure, radius of circle is 3.4 cm and perimeter of sector P-ABC is 12.8 cm . Find A(P-ABC).

Radius of the circle, r = 3.4 cm Perimeter of sector P-ABC = 12.8 cm Let l be the length of the arc ABC. ∴ l + 2r = 12.8 cm ⇒ l + 2 × 3.4 = 12.8 ⇒ l = 12.8 − 6.8 = 6 cm ∴ A(P-ABC) = Area of the sector PABC = 12lr=12×6×3.4 = 10.2 cm2 Thus, A(P-ABC) is 10.2 cm2.