Chapter 5

Perimeter and Area

Perimeter is the distance around a shape; area is the space inside, found with standard formulas for common 2-D shapes.

Perimeter

The perimeter is the total distance around the boundary of a flat shape. For a rectangle of length l and width w, perimeter P = 2(l + w). For a circle the perimeter is the circumference, C = 2πr = πd.

Area formulas

Key idea

Rectangle: A = l × w  |  Triangle: A = ½ × base × height  |  Parallelogram: A = base × height  |  Trapezium: A = ½(a + b) × h  |  Circle: A = πr²

Area is always measured in square units such as cm² or m². For a trapezium, a and b are the two parallel sides and h is the perpendicular distance between them.

Worked example

A trapezium has parallel sides 5 cm and 9 cm with a perpendicular height of 4 cm. Area = ½(5 + 9) × 4 = ½ × 14 × 4 = 28 cm². A circle of radius 7 cm (using π = 22/7) has area = 22/7 × 7² = 22/7 × 49 = 154 cm².

Compound shapes

Split a compound shape into rectangles, triangles and parts of circles, work out each area, then add or subtract as needed.

Remember

  • Use the perpendicular height in triangle and parallelogram formulas, not a slanted side.
  • Keep all lengths in the same unit before calculating.

In the examination, always write the formula, substitute the numbers, then give the answer with correct square units. For a compound shape such as an L-shape, cut it into two rectangles, find each area separately, and add them together.

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