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Area

Measurement · Area

Syllabus tag: KCSE | Mathematics | Form 1 | Topic 13 Area

Lesson objectives

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

  • State the units of area and convert from one to another.
  • Calculate the area of regular plane figures, including circles.
  • Calculate the area of composite figures.
  • Estimate the area of irregular shapes.

Area

Area measures the surface a flat shape covers. Every answer is in square units.

a) Units and converting

Converting area units Converting area units 1 m = 100 cm the length conversion 1 m² = 100 × 100 cm² square BOTH sides 1 m² = 10 000 cm² not 100 1 hectare = 10 000 m² a square 100 m by 100 m

This is the point that catches most learners. Because area multiplies two lengths, the conversion factor is squared.

So 1 m² is 10 000 cm², not 100.

Likewise 1 km² is 1 000 000 m².

A hectare is 10 000 m², used for land. 100 hectares make 1 km².

b) The formulas

Area formulas Area formulas rectangle = l × w length times width triangle = ½ × b × h perpendicular height parallelogram = b × h perpendicular height again trapezium = ½(a + b) × h average the parallel sides circle = π r² square the radius first

For the triangle and the parallelogram, the height must be perpendicular to the base, not the slanting side. Using the slant gives an answer that is too large.

For the trapezium, add the two parallel sides before halving. Halving only one is the usual slip.

For the circle, square the radius then multiply by π. If given the diameter, halve it first.

c) Circle: area against circumference

Circumference is 2πr and measures a length, in cm.

Area is πr² and measures a surface, in cm².

Confusing the two is the commonest error in circle questions. Check the units of your answer against what was asked.

d) Composite figures

Split the shape into parts you recognise. Work out each, then add.

Where a piece has been cut out, find the whole area and subtract the missing part.

Sketch the split and label each piece before calculating. It stops you counting a part twice or missing one.

Take a rectangle 10 cm by 6 cm with a semicircle of radius 3 cm on one end. The area is 60 + ½ × π × 9, which is about 74.1 cm².

e) Irregular shapes

Place the shape on a square grid.

Count every square wholly inside.

For part-squares, count those half covered or more; ignore the rest.

Add the two counts. The result is an estimate, and a finer grid gives a better one.

f) Where this is used

Buying paint, tiles or cloth. Measuring land in hectares. Costing a roof. Any question about covering a surface.

Words to know

  • Area -- the amount of surface covered by a plane figure, in square units.
  • Perpendicular height -- the height measured at right angles to the base.
  • Hectare -- a unit of land area equal to 10 000 m².
  • Composite figure -- a shape made from two or more simpler shapes.
  • Trapezium -- a quadrilateral with exactly one pair of parallel sides.

:::checkpoint Check yourself

  1. How many cm² are in 1 m²?
  2. Find the area of a trapezium with parallel sides 8 cm and 12 cm, and height 5 cm.
  3. Find the area of a circle of radius 7 cm, taking π as 22/7.
  4. Why is the conversion factor squared for area units? :::

Bridge to practice

The exercises begin with units and conversion, move through the standard formulae and circles, and finish with composite figures, paths and estimation. For every question involving a border, draw the inner and outer shapes separately before calculating anything.

Check yourselfPractise Area — 10 questions →Next in MathematicsVolume and Capacity →