How to find the area of a pentagon

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ACT Math › How to find the area of a pentagon

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Suppose the side length of a pentagon is . What is the area of the pentagon?

$4\sqrt{25+10\sqrt5}$

CORRECT

$\sqrt{25+10\sqrt5}$

$4\sqrt{5+5\sqrt5}$

$2\sqrt{5+5\sqrt5}$

$2\sqrt{10+10\sqrt5}$

Write the formula for the area of a pentagon.

$A=\frac{1}{4}s^2\sqrt{5(5+2\sqrt5)}$

Substitute the side length and simplify the radical.

$A=\frac{1}{4}(4)^2\sqrt{5(5+2\sqrt5)}$

$A=4\sqrt{5(5+2\sqrt5)}$

$A=4\sqrt{25+10\sqrt5}$