5.2 Area and Perimeter

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram, and trapezium.
  2. Remember that except for the area of a triangle, all other area formulas must be memorised — they are not given in the exam.

Part 1: Perimeter

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What is Perimeter?

Perimeter is the total distance around the outside of a shape. Think of it as walking all the way around the edge of a shape and measuring how far you've travelled.

Key rule: Perimeter = the sum of all the outer sides of a shape.

There is no single formula to memorise for perimeter. You simply add up every outer side.

Perimeter of a Rectangle

A rectangle has two pairs of equal sides: two sides of length L and two sides of width w.

P=L+L+w+w=2L+2w=2(L+w)P = L + L + w + w = 2L + 2w = 2(L + w)

Example: A rectangle has length 8 cm and width 3 cm.

P=2(8+3)=2×11=22 cmP = 2(8 + 3) = 2 \times 11 = 22 \text{ cm}

Perimeter of a Triangle

Add all three sides together.

Example: A triangle has sides 5 cm, 7 cm, and 9 cm.

P=5+7+9=21 cmP = 5 + 7 + 9 = 21 \text{ cm}

Perimeter of a Parallelogram

A parallelogram has two pairs of equal opposite sides. If the base is b and the slant side is s:

P=b+b+s+s=2b+2sP = b + b + s + s = 2b + 2s

Example: A parallelogram has a base of 10 cm and slant sides of 6 cm.

P=2(10)+2(6)=20+12=32 cmP = 2(10) + 2(6) = 20 + 12 = 32 \text{ cm}

Perimeter of a Trapezium

A trapezium has four sides — just add them all up. None of the sides are necessarily equal (unless told otherwise).

Example: A trapezium has sides 5 cm, 8 cm, 12 cm, and 7 cm.

P=5+8+12+7=32 cmP = 5 + 8 + 12 + 7 = 32 \text{ cm}

⚠️ Important: Composite Shapes and Perimeter

Sometimes a shape is made by joining two or more simpler shapes together. These are called composite shapes (or compound shapes).

When finding the perimeter of a composite shape, only count the outer sides. Any side that is shared on the inside between two shapes is not part of the perimeter.

Example: A triangle (sides 5, 5) sits on top of a rectangle (sides 4, 4, 8). The base of the triangle sits exactly on the top of the rectangle, so that shared side of length 8 is not an outer side.

P=5+5+4+8+4=26 cmP = 5 + 5 + 4 + 8 + 4 = 26 \text{ cm}

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