Perimeter and area for every shape in the Grade 8–9 syllabus — rectangles, squares, triangles, circles (and half-circles), plus composite shapes and working backwards from the area — each worked in full, with a worksheet.
Perimeter is the total distance around the outside of a shape (in units like cm). Area is the surface inside it (in square units like cm2). Each shape has its own formula — this guide works through all of them, plus the tricky exam cases: circles, composite shapes and reverse problems.
1The formulas to know
2Type 1: Rectangles and squares
- 1Perimeter = 2(l + b) = 2(8 + 5) = 2 × 13 = 26 cm.Add length and breadth, double it (two of each side).
- 2Area = l × b = 8 × 5 = 40 cm2.Area is in square units.
3Type 2: Triangles
- 1Area = 12 × base × height = 12 × 10 × 6.The height must be perpendicular to the base.
- 2= 12 × 60 = 30 cm2.
4Type 3: Circles
For a circle, r is the radius (centre to edge). The circumference is the circle's 'perimeter'. Use π ≈ 3,14 or the calculator's π button.
- 1Circumference = 2πr = 2 × 3,14 × 7 ≈ 43,96 cm.2πr goes around the edge.
- 2Area = πr2 = 3,14 × 72 = 3,14 × 49 ≈ 153,86 cm2.Square the radius FIRST, then multiply by π.
- 1Radius = diameter ÷ 2 = 20 ÷ 2 = 10 cm.The formulas need the radius, not the diameter.
- 2Area = π × 102 = 3,14 × 100 = 314 cm2.Always convert to radius first.
5Type 4: Composite shapes (add or subtract)
- 1Big rectangle area = 10 × 6 = 60 cm2.Find the whole shape first.
- 2Cut-out area = 4 × 3 = 12 cm2.Find the missing piece.
- 3Remaining area = 60 − 12 = 48 cm2.Subtract the cut-out from the whole.
6Type 5: Working backwards from the area
- 1Area = l × b, so 48 = 8 × b.Substitute what you know into the formula.
- 2b = 48 ÷ 8 = 6 cm.Rearrange: divide the area by the known side.
Diameter = 2 × radius. If a question gives the diameter, halve it before using any circle formula. For a semicircle, take half the full-circle area and add the straight diameter to the curved part for the perimeter.
Square only the radius in πr2. π × 72 means π × 49, not (π × 7)2. And keep units straight: perimeter/circumference in cm, area in cm2.
Measurement is guaranteed marks once the formulas are memorised. Practise every shape and the reverse questions in the worksheet below.
Practice exercises
Work each one out, then click to reveal the answer.
- 1Perimeter of a rectangle 8 cm by 5 cm (rectangle)
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2(8 + 5) = 26 cm - 2Area of a rectangle 8 cm by 5 cm (rectangle)
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8 × 5 = 40 cm2 - 3Perimeter and area of a square with side 6 cm (square)
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P = 4×6 = 24 cm; A = 62 = 36 cm2 - 4Area of a triangle, base 10 cm, height 6 cm (triangle)
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12 × 10 × 6 = 30 cm2 - 5Area of a triangle, base 14 cm, height 5 cm (triangle)
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12 × 14 × 5 = 35 cm2 - 6Circumference of a circle, radius 5 cm (π ≈ 3.14) (circle)
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2 × 3.14 × 5 = 31.4 cm - 7Area of a circle, radius 10 cm (π ≈ 3.14) (circle)
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3.14 × 100 = 314 cm2 - 8Area of a circle with DIAMETER 12 cm (π ≈ 3.14) (circle)
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r = 6; 3.14 × 36 = 113.04 cm2 - 9A 10×8 rectangle with a 3×2 rectangle cut out — area? (composite)
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80 − 6 = 74 cm2 - 10A rectangle has area 60 cm2 and breadth 5 cm. Find its length. (reverse)
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60 ÷ 5 = 12 cm
Quick Quiz
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