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Chapter 1: Problem 36

Find the perimeter and area of each figure. a square with length 12 feet

Short Answer

Expert verified
The perimeter is 48 feet and the area is 144 square feet.

Step by step solution

01

Identify the Formula for Perimeter

For a square, the perimeter is calculated by adding up all four sides. Since all sides of a square are equal, the formula to calculate the perimeter is \( 4 \times \text{side length} \).
02

Calculate the Perimeter

Given that the side length of the square is 12 feet, substitute this value into the formula: \( 4 \times 12 = 48 \). Thus, the perimeter of the square is 48 feet.
03

Identify the Formula for Area

The area of a square is found by squaring the side length. The formula is \( \text{side length}^2 \).
04

Calculate the Area

Using the side length of 12 feet, compute the area: \( 12^2 = 144 \). Therefore, the area of the square is 144 square feet.

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Key Concepts

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

Understanding Perimeter
The perimeter of a shape is the total distance around the boundary of that shape.
When dealing with a square, it's important to remember that all sides are equal.
This makes calculating the perimeter super simple!
  • The perimeter is found by adding up all four sides of the square.
  • Because each side is of the same length, you can also find the perimeter by multiplying one side by four.
So, for a square with a side length of 12 feet, the perimeter can be calculated as follows: \[P = 4 \times 12 = 48 \, \text{feet}\] Hence, the perimeter of this square is 48 feet.
Calculating Area
Calculating the area of a shape helps you understand how much surface the shape covers.
For a square, this is especially straightforward because the area only depends on the side length.
  • To find the area of a square, simply multiply the length of one side by itself (squared).
  • This multiplication tells you how many square units fit within the square.
As given in the exercise, if each side of our square is 12 feet long, the calculation for area is: \[A = 12 \times 12 \] This equals 144 square feet.
Therefore, the area of our square is 144 square feet.
Properties of a Square
A square is a special type of polygon that comes with unique properties.
Understanding these can help simplify many mathematical calculations.
  • All four sides of a square are of equal length.
  • Each of the four angles is a right angle (90 degrees), making the square a rectangle as well.
  • The opposite sides are parallel, which is another characteristic of rectangles.
These properties make it easy to apply formulas for both perimeter and area, as shown in previous sections.
Knowing this, you can quickly solve similar problems with any square's side length!

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