math · 32 minutes · Official OETT Aligned
Area & Shapes
Find how much surface a shape covers
What to know
- area: space inside a flat shape
- rectangle, triangle, and circle
- splitting a complex shape into simpler parts
- square feet or square inches
Questions about floor space, paint, or surface coverage usually need area.
The core rule
Choose the formula for the shape. Give area in square units, such as square feet.
Rectangle: length × width. Triangle: base × height ÷ 2, using the height at a right angle to the base. Circle: π × radius × radius, with π about 3.14. Split an unusual floor plan into simple shapes, then add their areas without counting any space twice.
Worked examples
Example 1: easy
A 14 ft by 9 ft rectangle has 126 sq ft.
- Use rectangle area A = L × W with 14 ft and 9 ft.
- Calculate 14 × 9 = 126 and label square feet.
Area counts how many square units fit inside the shape.
Example 2: medium
A triangle with base 12 ft and height 7 ft has 42 sq ft.
- Use triangle area A = 1/2bh with base 12 ft and perpendicular height 7 ft.
- Calculate 1/2 × 12 × 7 = 42 square feet.
A triangle has half the area of a rectangle with the same base and height.
Example 3: hard
A 10×8 rectangle plus a 4×3 extension has 92 sq ft.
- Find the main rectangle: 10 × 8 = 80 square feet.
- Find the extension: 4 × 3 = 12 square feet; add 80 + 12 = 92 square feet.
Add the two areas because they do not overlap.
Common mistakes
Add the sides whenever a shape has measurements.
Adding the sides gives the distance around the shape. Area measures the space inside it.
Put it into practice
Use guided explanations, check your answers, and try a new variation.