Perimeter and area

Perimeter and area of rectangles, triangles, trapezia and compound shapes.

  • Define and explain Perimeter and area in your own words
  • Use key terms such as Perimeter accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Perimeter and area: perimeter and area of rectangles, triangles, trapezia and compound shapes.

Definition: Perimeter and area

Perimeter and area of rectangles, triangles, trapezia and compound shapes.

Key ideas

Area formulae

Rectangle: base times height. Triangle: half times base times height, using the perpendicular height, not the slant side. Trapezium: half times the sum of the parallel sides times the distance between them.

Circles

Circumference equals pi times diameter (C = πd), and area equals pi times radius squared (A = πr²). Do not mix them up: circumference is a length, area is measured in square units.

Key term — Perimeter: The total distance around the edge of a 2D shape, found by adding all its side lengths.

Worked example: Perimeter and area

Find the perimeter and area of a rectangle 7 cm by 4 cm.

Perimeter = 2(7 + 4) = 22 cm; area = 7 × 4 = 28 cm².

Answer: Perimeter = 2(7 + 4) = 22 cm; area = 7 × 4 = 28 cm².

Common mistakes
  • Forgetting units squared for area Area is measured in square units (cm²); perimeter is a length (cm). Always state the right unit.
  • Confusing radius and diameter in circle formulae A = πr² uses the radius; C = πd uses the diameter. If given the diameter, halve it first for area.

Practice

A triangle has base 10 cm and perpendicular height 6 cm. Find its area.
Area = ½ × base × height.

Area = ½ × 10 × 6 = 30 cm².

A trapezium has parallel sides 8 cm and 5 cm, with height 4 cm. Find its area.
Area = ½ × (sum of parallel sides) × height.

Area = ½ × (8 + 5) × 4 = ½ × 13 × 4 = 26 cm².

A circle has radius 5 cm. Find its area (use π = 3.14).
A = πr² — square the radius first.

A = 3.14 × 25 = 78.5 cm².

Two angles on a straight line are 112° and x. Find x.
Angles on a straight line sum to 180°.

x = 180 − 112 = 68°.

Quick check

Perimeter and area — quick check

Which of these best defines "Perimeter"?

The total distance around the edge of a 2D shape, found by adding all its side lengths.

Find the circumference of a circle with diameter 14 cm (use π = 3.14).

C = 3.14 × 14 = 43.96 cm.
Key takeaways
  • Perimeter and area: perimeter and area of rectangles, triangles, trapezia and compound shapes.
  • Area formulae: Rectangle: base times height.
  • Angle: The amount of turn between two lines that meet, measured in degrees.
  • Watch out for: forgetting units squared for area