Area · Grade 9

In Grade 9 you learn: sectors and composite shapes.

Area is the amount of flat space a shape covers, measured in square units such as cm² and m². Count the squares, or use the formula for the shape; a compound shape splits into simpler shapes.

Key facts

  • Area is measured in square units: count the squares a shape covers.
  • Rectangle: area = length × width; perimeter = 2 × (length + width).
  • Triangle: area = ½ × base × perpendicular height.
  • Parallelogram: area = base × perpendicular height.
  • Trapezoid: area = ½ × (a + b) × h, where a and b are the parallel sides.
  • Compound shapes: split into rectangles (or subtract a missing piece). Use the same units throughout.

Worked examples

Example 1

A circle has a radius of 5 cm. Find its area to 1 decimal place.

Answer: 78.5 cm²

Example 2

Find the area of a parallelogram with a base of 8 cm and a perpendicular height of 5 cm.

Answer: 40 cm²

Example 3

A trapezoid has parallel sides of 7 cm and 11 cm and a height of 4 cm. Find its area.

Answer: 36 cm²

Example 4

A right triangle with shorter sides 4 cm and 3 cm is cut from a rectangle 12 cm by 5 cm. Find the area left.

Answer: 54 cm²

Example 5

A rectangle has an area of 48 cm² and a perimeter of 28 cm. Find its length and width.

Answer: 8 cm, 6 cm

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