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 inside a flat shape, measured in square units.

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 measures how much surface is covered inside a boundary.

Common stuck point: The procedure for area is the easy part; the trap is using area for a border problem. Asking "Am I counting unit squares inside the shape?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I counting unit squares inside the shape?

Worked Examples

Example 1

easy
Find the area of a rectangle with length 1212 cm and width 77 cm.

Answer

A=84 cm2A = 84 \text{ cm}^2

First step

1
Recall the area formula for a rectangle: A=l×wA = l \times w.

Full solution

  1. 2
    Substitute: A=12×7=84A = 12 \times 7 = 84 cm².
  2. 3
    The area is 8484 square centimetres.
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 1010 cm and height 66 cm.

Example 3

medium
Find the area of a trapezoid with parallel sides 88 cm and 1212 cm, and height 55 cm.

Example 4

easy
A rectangular sticker is 33 cm by 55 cm. What is its area?

Example 5

hard
A square has the same area as a rectangle of dimensions 16×916 \times 9. Find the square's side.

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 88 cm and 1414 cm, and a height of 55 cm. Find its area.

Example 2

medium
A parallelogram has base 1212 cm and area 8484 cm². Find its height.

Example 3

easy
Find the area of a rectangle with length 77 and width 44.

Example 4

easy
Find the area of a square with side 55 cm.

Example 5

easy
A rectangle has area 2424 and length 66. Find its width.

Example 6

easy
A square has area 3636 cm². Find its side.

Example 7

easy
Find the area of a triangle with base 88 and height 55.

Example 8

easy
Find the area of a rectangle with length 1212 cm and width 99 cm.

Example 9

easy
How many square inches are in 11 square foot?

Example 10

easy
Find the area of an L-shape: a 6×46 \times 4 rectangle with a 2×22 \times 2 square cut from one corner.

Example 11

medium
A garden is a rectangle 2020 ft by 1515 ft. What is its area?

Example 12

medium
A triangular sail has base 44 m and height 77 m. Find its area.

Example 13

medium
A rectangular room is 1414 ft by 1010 ft. Carpet costs $5\$5 per square foot. How much to carpet the room?

Example 14

medium
Find the area of a parallelogram with base 1010 and height 66.

Example 15

medium
Find the area of a trapezoid with parallel sides 55 and 99, and height 44.

Example 16

medium
A rectangle has perimeter 3030 and area 5454. Find length and width.

Example 17

medium
Find the area of a right triangle with legs 55 and 1212.

Example 18

medium
A rectangle has area 7272. List all possible integer (length, width) pairs with length ≥\geq width.

Example 19

medium
Find the area of an equilateral triangle with side 66.

Example 20

challenge
A path of uniform width 11 ft surrounds a 10×1510 \times 15 ft garden. Find the area of the path.

Example 21

challenge
Among all rectangles with perimeter 2020, which has the largest area?

Example 22

challenge
A right triangle has area 2424 and one leg 66. Find its hypotenuse.

Example 23

easy
Find the area of a rectangle with length 99 cm and width 55 cm.

Example 24

easy
Find the area of a square with side 88 in.

Example 25

easy
Find the area of a triangle with base 66 and height 99.

Example 26

easy
Find the area of a parallelogram with base 77 and height 44.

Example 27

medium
Find the area of a trapezoid with parallel sides 66 and 1010 and height 44.

Example 28

medium
A rectangle is 1515 m long and has area 9090 m². Find its width.

Example 29

medium
A triangle has area 4040 and base 1010. Find the height.

Example 30

medium
A bedroom is 1212 ft by 1111 ft. Carpet costs $4 per square foot. How much does it cost to carpet the room?

Example 31

medium
Find the area of an L-shape made by joining a 5×85 \times 8 rectangle and a 3×43 \times 4 rectangle (no overlap).

Example 32

medium
A rectangle has perimeter 2424 and length 77. Find its area.

Example 33

medium
Find the area of a right triangle with legs 99 and 1212.

Example 34

medium
A trapezoid has area 4848, parallel sides 66 and 1010. Find its height.

Example 35

medium
Convert: 11 m² equals how many cm²?

Example 36

hard
A rectangle has area 9696 and perimeter 4040. Find its dimensions.

Example 37

hard
A path of uniform width 22 ft surrounds a 20×1220 \times 12 ft garden. Find the area of the path.

Example 38

hard
An equilateral triangle has side 1010. Find its area in simplest radical form.

Example 39

hard
A rectangle's length is doubled and its width is tripled. How does the area change?

Example 40

hard
Find the area of a triangle with vertices (0,0)(0,0), (6,0)(6,0), (0,8)(0,8).

Example 41

challenge
A rectangle has area 6060 and one side 55 longer than the other. Find both sides.

Example 42

challenge
Among all rectangles with perimeter 3636, find the maximum area.
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Background Knowledge

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

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