Area Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Area.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The amount of two-dimensional space enclosed inside a flat shape, measured in square units. For rectangles, area equals length times width; for triangles, it is half the base times height; and for circles, \pi r^2. Area answers the question: how much surface does this shape cover?

How many unit squares would you need to tile the inside of the shape completely, with no gaps?

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Area is two-dimensional—measured in square units like cm² or ft², not linear units.

Common stuck point: Units are squared (\text{ft}^2, \text{m}^2) because it's 2D.

Sense of Study hint: Draw the shape on grid paper and count the unit squares inside to check your formula answer.

Worked Examples

Example 1

easy
Find the area of a rectangle with length 12 cm and width 7 cm.

Solution

  1. 1
    Recall the area formula for a rectangle: A = l \times w.
  2. 2
    Substitute: A = 12 \times 7 = 84 cm².
  3. 3
    The area is 84 square centimetres.

Answer

A = 84 \text{ cm}^2
The area of a rectangle equals the product of its length and width. Area is always measured in square units because it represents two-dimensional space.

Example 2

medium
Find the area of a triangle with base 10 cm and height 6 cm.

Example 3

medium
Find the area of a trapezoid with parallel sides 8 cm and 12 cm, and height 5 cm.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A trapezoid has parallel sides of 8 cm and 14 cm, and a height of 5 cm. Find its area.

Example 2

medium
A parallelogram has base 12 cm and area 84 cm². Find its height.

Background Knowledge

These ideas may be useful before you work through the harder examples.

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