Area and Perimeter Explained

Area and perimeter both measure shapes, but they measure different things. Mixing them up is one of the most common geometry mistakes.

Quick idea

Perimeter measures distance around a shape. Area measures the space inside a shape.

Steps

1. Identify whether the question asks for around or inside.
2. Use perimeter formulas for distance around the boundary.
3. Use area formulas for square units inside the shape.
4. Label perimeter with units and area with square units.

Worked example

Find the area and perimeter of a rectangle with length 8 and width 3.

Full solution

Step-by-step walkthrough

Step 1

Area is length times width, so the area is 24 square units.

Step 2

Perimeter adds all side lengths, so the perimeter is 22 units.

Step 3

The units are different because they measure different things.

Common mistake

Area uses square units, like square inches. Perimeter uses normal units, like inches.

Practice problems

1. Find the area of a 5 by 7 rectangle.
2. Find the perimeter of a 5 by 7 rectangle.
3. A square has side 6. Find its area.

Answers

1. 35 square units
2. 24 units
3. 36 square units

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Find the Area of a Triangle
• How to Find Circumference and Area of a Circle
• Pythagorean Theorem Explained