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Chapter 9: Problem 13

Find the perimeter of each square. $$ 45.5 \mathrm{~mm} \text { on a side } $$

Short Answer

Expert verified
The perimeter of the square is 182 mm.

Step by step solution

01

- Understand the Problem

A square has four equal sides. To find the perimeter of a square, add up the lengths of all four sides.
02

- Formula for Perimeter of a Square

The formula for the perimeter (\text{P}) of a square with side length (\text{s}) is: \[ P = 4 \times s \]
03

- Plug in the Given Value

Here, the side length (\text{s}) is 45.5 mm. Plug in the value into the formula: \[ P = 4 \times 45.5 \text{ mm} \]
04

- Calculation

Perform the multiplication: \[ P = 4 \times 45.5 = 182 \text{ mm} \]
05

- Conclusion

The perimeter of the square is 182 mm.

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Key Concepts

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

square geometry
In geometry, a square is a special type of quadrilateral. It has four equal sides and four right angles.
Every angle in a square is 90 degrees.
This symmetry gives the square some unique properties.
One of the key properties of a square is that all sides are the same length. Knowing this makes calculations easier and more straightforward.
Each diagonal in a square bisects it into two congruent right-angled triangles.
Understanding these basic properties helps in solving many problems related to square geometry.
perimeter calculation
The perimeter of a shape is the total length around it.
For squares, adding all four side lengths gives us the perimeter.
Because all sides are equal, the formula simplifies.
The formula for the perimeter (P) of a square with side length (s) is: \[ P = 4 \times s \] This means you just multiply the side length by 4.
Here鈥檚 a quick step-by-step process:
  • Identify the length of one side.
  • Multiply that length by 4.
  • The result is the perimeter.
This simplicity makes it easy to find the perimeter when you know the side length.
mathematical formulas
Mathematical formulas are essential tools in geometry.
They help us find measurements like area, perimeter, and volume quickly.
For a square, the key formulas you should remember are:
  • Perimeter: \[ P = 4 \times s \]
  • Area: \[ A = s^2 \]
Plugging values into these formulas lets you solve problems efficiently.
Here鈥檚 how formulas work with an example: If a square has a side length of 45.5 mm, you use the perimeter formula: \[ P = 4 \times 45.5 \]
Calculate it to find \[ P = 182 \text{ mm} \]
This step-by-step approach ensures accuracy and clear understanding.

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