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Chapter 23: Chapter 23

Problem 442

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Find the area of a square whose perimeter is \(20 \mathrm{ft}\).

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The area of a square with a perimeter of \(20 \mathrm{ft}\) is \(25 \mathrm{ft}^2\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Determine the side length of the square

Since the perimeter of a square is given by the formula \(P = 4s\), where \(P\) is the perimeter and \(s\) is the side length, we can find the side length by dividing the perimeter by 4: \[s = \frac{P}{4}\] Given the perimeter \(P = 20 \mathrm{ft}\), we can plug in the value and find the side length: \[s = \frac{20 \mathrm{ft}}{4} \] \[s = 5 \mathrm{ft}\] Now we know the side length of the square is \(5 \mathrm{ft}\).

Step 2: Calculate the area of the square

To find the area of a square, we can use the formula \(A = s^2\), where \(A\) is the area and \(s\) is the side length. We know that the side length of the square is \(5 \mathrm{ft}\), so we can plug in the value to find the area: \[A = (5 \mathrm{ft})^2\] \[A = 25 \mathrm{ft}^2\] Hence, the area of the square is \(25 \mathrm{ft}^2\).

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Most popular questions from this chapter

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