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Find the area of a regular pentagon that is inscribed in a circle of radius 3. Round to the nearest whole number.

Sagot :

Answer:

The area of the pentagon is approximately 21 square units

Step-by-step explanation:

The radius of the circle in which the regular pentagon is inscribed, r = 3

The area of a pentagon, 'A', inscribed in a circle with radius, r is given as follows;

A = 5×(1/2) ×2×r·sin(32°)×r·cos(32°) = (5/2)×r²×sin(72°)

Therefore, the area of the pentagon, A = (5/2)×3²×sin(72°) ≈ 21.3987716166 ≈  21

The area of the pentagon, A ≈ 21 square units.

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