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Area and Perimeter: Definition and Example | EDU.COM

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Area and Perimeter: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Area and PerimeterArea and Perimeter: Definition and ExampleTable of ContentsArea and Perimeter Definition of Area and Perimeter

Perimeter is the total distance around a 222-dimensional shape. For shapes with straight sides like triangles, rectangles, squares, or polygons, we calculate the perimeter by adding up the lengths of all sides. When we look at a shape, the perimeter represents the boundary or outer edge of that shape, like the fence around a park.

Area is the space enclosed within the perimeter of a 222-dimensional shape. Think of area as the amount of surface inside a shape. To find the area of different shapes, we use specific formulas depending on the number of sides and the angles between those sides. For example, a triangle's area is calculated using 12×base×height\frac{1}{2} \times \text{base} \times \text{height}21​×base×height, while a square's area is found using side×side\text{side} \times \text{side}side×side.

Examples of Area and Perimeter Example 1: Finding the Height of a Triangle Problem:

The area of a triangle with a base of 777 units is 212121 square units. What is the height of the triangle?

triangle

Step-by-step solution:

Step 1, Write the formula for the area of a triangle. The area equals 12×base×height\frac{1}{2} \times \text{base} \times \text{height}21​×base×height.

Step 2, Plug in the known values into the formula. We know the area is 212121 square units and the base is 777 units.

21=12×7×height21 = \frac{1}{2} \times 7 \times \text{height}21=21​×7×height

Step 3, Solve for the height by multiplying both sides by 222 and then dividing by the base.

height=2×areabase=2×217=427=6 units\text{height} = \frac{2 \times \text{area}}{\text{base}} = \frac{2 \times 21}{7} = \frac{42}{7} = 6 \text{ units}height=base2×area​=72×21​=742​=6 units

Step 4, Therefore, the height of the triangle is 666 units.

Example 2: Finding the Area of a Triangle Problem:

What is the area of a triangle with a base of 666 units and a height of 101010 units?

triangle

Step-by-step solution:

Step 1, Write the formula for the area of a triangle. The area equals 12×base×height\frac{1}{2} \times \text{base} \times \text{height}21​×base×height.

Step 2, Plug in the known values into the formula. We know the base is 666 units and the height is 101010 units.

Area=12×6×10\text{Area} = \frac{1}{2} \times 6 \times 10Area=21​×6×10

Step 3, Calculate the area by multiplying the numbers.

Area=12×60=30 square units\text{Area} = \frac{1}{2} \times 60 = 30 \text{ square units}Area=21​×60=30 square units

Step 4, Therefore, the area of the triangle is 303030 square units.

Example 3: Finding the Perimeter of a Square from its Area Problem:

If the area of a square is 363636 square centimeters, what is its perimeter?

square

Step-by-step solution:

Step 1, Find the side length of the square using the area formula. For a square, area equals side×side\text{side} \times \text{side}side×side.

36=side×side=side236 = \text{side} \times \text{side} = \text{side}^236=side×side=side2

Step 2, Take the square root of the area to find the side length.

side=36=6 cm\text{side} = \sqrt{36} = 6 \text{ cm}side=36​=6 cm

Step 3, Calculate the perimeter using the formula for a square: perimeter equals 4×side4 \times \text{side}4×side.

Perimeter=4×6=24 cm\text{Perimeter} = 4 \times 6 = 24 \text{ cm}Perimeter=4×6=24 cm

Step 4, Therefore, the perimeter of the square is 24 cm24 \text{ cm}24 cm.

Comments(7)SSoftballDevoteeTheoNovember 6, 2025I've used this glossary page to teach area and perimeter. The examples are super helpful, making it easy for students to grasp these concepts!

SSoccerPlayerKaiNovember 5, 2025I've used this glossary page to teach area and perimeter. The examples are super helpful. My students finally get it! Thanks!

MCMs. CarterSeptember 16, 2025I’ve used the Area and Perimeter examples on this page to help my kids with their homework, and they finally get it! The step-by-step explanations made it so easy to understand. Great resource!

NNatureLover123September 10, 2025I’ve been using this page to help my kids with their math homework, and it’s been a lifesaver! The examples are super clear, especially for explaining area and perimeter with shapes like triangles and squares.

MCMs. CarterAugust 27, 2025I’ve used the area and perimeter examples from this page to help my kids with their math homework. The step-by-step explanations made it so much easier for them to understand!

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