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 12 cm and width 7 cm.Rectangle with length 12 cm and width 7 cm
Answer
A=84 cm2
First step
1
Recall the area formula for a rectangle: A=l×w.
Full solution
2
Substitute: A=12×7=84 cm².
3
The area is 84 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 10 cm and height 6 cm.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.Trapezoid with parallel sides 8 cm and 12 cm, height 5 cm
Example 4
easy
A rectangular sticker is 3 cm by 5 cm. What is its area?
Example 5
hard
A square has the same area as a rectangle of dimensions 16×9. 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 8 cm and 14 cm, and a height of 5 cm. Find its area.Trapezoid with parallel sides 8 cm and 14 cm, height 5 cm
Example 2
medium
A parallelogram has base 12 cm and area 84 cm². Find its height.
Example 3
easy
Find the area of a rectangle with length 7 and width 4.Rectangle with length 7 and width 4
Example 4
easy
Find the area of a square with side 5 cm.Square with side 5 cm
Example 5
easy
A rectangle has area 24 and length 6. Find its width.
Example 6
easy
A square has area 36 cm². Find its side.
Example 7
easy
Find the area of a triangle with base 8 and height 5.Triangle with base 8 and height 5
Example 8
easy
Find the area of a rectangle with length 12 cm and width 9 cm.
Example 9
easy
How many square inches are in 1 square foot?
Example 10
easy
Find the area of an L-shape: a 6×4 rectangle with a 2×2 square cut from one corner.
Example 11
medium
A garden is a rectangle 20 ft by 15 ft. What is its area?
Example 12
medium
A triangular sail has base 4 m and height 7 m. Find its area.Triangular sail with base 4 m and height 7 m
Example 13
medium
A rectangular room is 14 ft by 10 ft. Carpet costs $5 per square foot. How much to carpet the room?
Example 14
medium
Find the area of a parallelogram with base 10 and height 6.Parallelogram with base 10 and height 6
Example 15
medium
Find the area of a trapezoid with parallel sides 5 and 9, and height 4.Trapezoid with parallel sides 5 and 9, height 4
Example 16
medium
A rectangle has perimeter 30 and area 54. Find length and width.
Example 17
medium
Find the area of a right triangle with legs 5 and 12.
Example 18
medium
A rectangle has area 72. List all possible integer (length, width) pairs with length ≥ width.
Example 19
medium
Find the area of an equilateral triangle with side 6.Equilateral triangle with side length 6
Example 20
challenge
A path of uniform width 1 ft surrounds a 10×15 ft garden. Find the area of the path.
Example 21
challenge
Among all rectangles with perimeter 20, which has the largest area?
Example 22
challenge
A right triangle has area 24 and one leg 6. Find its hypotenuse.
Example 23
easy
Find the area of a rectangle with length 9 cm and width 5 cm.Rectangle with length 9 cm and width 5 cm
Example 24
easy
Find the area of a square with side 8 in.
Example 25
easy
Find the area of a triangle with base 6 and height 9.Triangle with base 6 and height 9
Example 26
easy
Find the area of a parallelogram with base 7 and height 4.Parallelogram with base 7 and height 4
Example 27
medium
Find the area of a trapezoid with parallel sides 6 and 10 and height 4.Trapezoid with parallel sides 6 and 10, height 4
Example 28
medium
A rectangle is 15 m long and has area 90 m². Find its width.
Example 29
medium
A triangle has area 40 and base 10. Find the height.
Example 30
medium
A bedroom is 12 ft by 11 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 5×8 rectangle and a 3×4 rectangle (no overlap).
Example 32
medium
A rectangle has perimeter 24 and length 7. Find its area.
Example 33
medium
Find the area of a right triangle with legs 9 and 12.
Example 34
medium
A trapezoid has area 48, parallel sides 6 and 10. Find its height.Trapezoid with parallel sides 6 and 10; find height h
Example 35
medium
Convert: 1 m² equals how many cm²?
Example 36
hard
A rectangle has area 96 and perimeter 40. Find its dimensions.
Example 37
hard
A path of uniform width 2 ft surrounds a 20×12 ft garden. Find the area of the path.
Example 38
hard
An equilateral triangle has side 10. Find its area in simplest radical form.Equilateral triangle with side length 10
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), (6,0), (0,8).
Example 41
challenge
A rectangle has area 60 and one side 5 longer than the other. Find both sides.
Example 42
challenge
Among all rectangles with perimeter 36, find the maximum area.