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Chapter 0: Problem 6

Find the perimeter and area of a square with side \(8 \mathrm{ft}\).

Short Answer

Expert verified
The perimeter is 32 ft and the area is 64 ft虏.

Step by step solution

01

Identify the side length of the square

The side length of the square is given as 8 feet.
02

Calculate the perimeter

The formula for the perimeter of a square is given by \( P = 4s \), where \( s \) is the side length. Substituting the side length: \( P = 4 \times 8 \) which gives \( P = 32 \mathrm{ft} \).
03

Calculate the area

The formula for the area of a square is \( A = s^2 \). Substituting the side length: \( A = 8^2 \) which gives \( A = 64 \mathrm{ft^2} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Square Geometry
A square is a simple geometric shape which has four equal sides and four right angles.
Each angle in a square is 90 degrees, making it a type of rectangle.
One important thing to remember is that all sides of a square are of the same length, which makes it easy to calculate various properties.
Understanding these fundamental characteristics is essential when solving problems that involve squares.

Consider a square with a side length of 8 feet. Knowing that all sides are equal helps simplify both the perimeter and area calculations you'll make.
Perimeter Calculation
The perimeter of a square is the total length of its boundary.
Since all four sides are equal, calculating the perimeter becomes straightforward.

The formula to find the perimeter of a square is:
\( P = 4s \)
where \( P \) is the perimeter and \( s \) is the side length.
In our case, with a side length of 8 feet:
\( P = 4 \times 8 \)
which simplifies to
\( P = 32 \text{ feet} \).

These simple steps help you to find the perimeter quickly and correctly.
Always remember that for any square, you just have to multiply the side length by 4 to get the perimeter.
Area Calculation
The area of a square is the amount of space enclosed within its four sides.
To calculate the area, we use the length of one side and square it.

The formula for the area of a square is:
\( A = s^2 \)
where \( A \) is the area and \( s \) is the side length.
For a square with a side length of 8 feet:
\( A = 8^2 \)
which simplifies to
\( A = 64 \text{ square feet} \).

Hence, the area tells us that 64 square feet are enclosed by the 8-foot sides of the square.
Remember, squaring the side length gives you a direct way to find the area for any square.

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Most popular questions from this chapter

Find the length of the sides of a rhombus with diagonals \(12^{\prime \prime}\) and \(18^{\prime \prime}\).

A side of one rectangle is \(25 \mathrm{ft}\) and the corresponding side of a second similar rectangle is \(10 \mathrm{ft}\). If the perimeter of the first rectangle is \(150 \mathrm{ft}\) and its area is 1250 sq ft, find the perimeter and area of the similar rectangle.

Find the perimeter and area of a semicircle with radius 10 in.

Consider a cube of side \(x\) (a) Show that the surface area of a cube of side \(x\) is \(S=6 x^{2}\) (b) If the edge of a cube is doubled in length, what happens to the surface area? To the volume? [Hint: Consider the ratio of the original surface area to the new surface area, and similarly for the volumes.] (c) If the edge of a cube is tripled in length, what happens to the surface area? To the volume? [Hint: Consider the ratio of the original surface area to the new surface area, and similarly for the volumes.] (d) Can you generalize the results of parts (b) and (c) to describe what happens to the surface area and volume of a cube if the length of its edge is multiplied by \(k ?\)

Answers should be rounded to the nearest tenth unless otherwise indicated. How much water is needed to fill a cylindrical swimming pool of diameter \(4 \mathrm{m}\) to a height of \(1.4 \mathrm{m} ?\)
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