Question

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jody buys 20 yards of fencing to build a garden. the garden will have 5 sides. what is the area of the largest garden she can build?
the 5 - sided figure with the largest area for a given perimeter is a pentagon. since jody has 20 yards of fencing, the sides of the figure must measure approximately square yards.
the area of the garden will be

Explanation:

Step1: Find side length of pentagon

Perimeter $P=20$ yards, 5 sides. Side length $s=\frac{P}{5}=\frac{20}{5}=4$ yards.

Step2: Use regular pentagon area formula

Area formula: $A=\frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^2$
Substitute $s=4$:
$A=\frac{1}{4}\sqrt{5(5+2\sqrt{5})}\times4^2$

Step3: Calculate the value

First compute $\sqrt{5}\approx2.236$, so $5+2\sqrt{5}\approx5+4.472=9.472$
$5\times9.472=47.36$, $\sqrt{47.36}\approx6.882$
$4^2=16$, so $A=\frac{1}{4}\times6.882\times16=6.882\times4\approx27.53$

Answer:

The 5-sided figure with the largest area for a given perimeter is a regular pentagon. Since Jody has 20 yards of fencing, the sides of the figure must measure 4 yards. The area of the garden will be approximately 27.5 square yards.