What are area and perimeter?
Perimeter is the distance around a shape. Area is the amount of space inside a shape. We use formulas to calculate each one for different shapes.
Key formulas to remember
- Rectangle: Area = length × width; Perimeter = 2 × (length + width)
- Square: Area = side²; Perimeter = 4 × side
- Triangle: Area = 1/2 × base × height; Perimeter = sum of all three sides
- Circle: Area = π × radius²; Circumference (perimeter) = 2π × radius
Step-by-step approach
- Understand the problem and identify the shape you are dealing with.
- Write down the given measurements (length, width, base, height, etc.).
- Choose the right formula for either area or perimeter.
- Plug in the numbers and compute. Remember: area units are squared (cm², m²), while perimeter units stay as the length unit (cm, m).
- Check your answer: are the units correct? Does the size make sense for the shape?
Practice problems
Problem 1: Rectangle
A rectangle is 6 cm long and 4 cm wide. Find its area and its perimeter.
- Area = 6 × 4 = 24 cm²
- Perimeter = 2 × (6 + 4) = 20 cm
Problem 2: Rectangle with a missing side
A rectangle has area 36 cm² and width 6 cm. Find the length. Then compute the perimeter.
- Length = Area ÷ Width = 36 ÷ 6 = 6 cm
- Perimeter = 2 × (6 + 6) = 24 cm
Problem 3: Triangle
A triangle has base 8 cm and height 5 cm. What is its area?
- Area = 1/2 × base × height = 1/2 × 8 × 5 = 20 cm²
Tips:
- When a side is missing, use the perimeter formula to solve for it, or the area formula to solve for the height/base.
- Keep track of units. Area uses square units (cm², m²). Perimeter uses linear units (cm, m).
- Estimate: if numbers look off, re-check calculations and units.