Area

2.0 Measurement · 2.2 Area

Syllabus tag: Kenya CBC | Grade 6 Mathematics | Strand 2.0 Measurement | Sub-Strand 2.2 Area (6 Lessons)

Lesson objectives

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

Work out the area of triangles in square centimetres (cm²)
Work out the area of combined shapes involving squares, rectangles, and triangles
Estimate the area of circles by counting squares
Appreciate the use of cm² in working out area in real life

Area measures the flat space inside a shape. We count it in square centimetres, written cm².

One cm² is a square measuring 1 cm on every side.

a) Why a triangle is half

Draw a rectangle. Now draw one diagonal across it.

The diagonal cuts the rectangle into two triangles of exactly the same size.

So each triangle is half the rectangle. That is where the rule comes from.

b) Area of a triangle

The rule is area = ½ × base × height.

The height must be the straight-up distance from the base to the top point. It is not the slanting side.

Multiply the base by the height first, then halve. Halving before multiplying works too, but only if you halve one number, not both.

c) Combined shapes

Some shapes are made of simpler ones joined together.

Split the shape into parts you recognise. Work out each part. Then add them.

Sketch the split first and mark each piece. It stops you missing a part or counting one twice.

Sometimes it is easier to subtract. If a piece is cut out, find the whole area and take away the missing bit.

d) Estimating the area of a circle

A circle has no straight sides, so we estimate by counting squares.

Draw the circle on squared paper.

Count every square that is completely inside. Then look at the part-squares. Count one if it is half covered or more. Ignore it if less than half.

Add the two counts. That is your estimate.

Smaller squares give a better estimate, because fewer squares are part-covered.

e) Always square units

Area answers are in cm² or m², never cm or m.

If your answer has no small 2, it is a length, not an area.

f) Where this is used

Working out how much cloth covers a table. Counting tiles for a floor. Finding how much paint a wall needs. Measuring a garden plot.

Words to know

Area — the amount of surface a flat shape covers, measured in square units (e.g. cm²).
Base and height (of a triangle) — the side used as the "bottom," and the straight-line distance from that side to the opposite corner, at a right angle.
Combined shape — a shape made of two or more simple shapes joined together.

:::checkpoint Check yourself

Find the area of a triangle with base 10 cm and height 6 cm.
Why is a triangle half of a rectangle?
When counting squares, what do you do with a square that is only a quarter covered?
What units does area use? :::

Try the exercises below — triangle area, combined shapes, and real-life area problems, the same skills covered above.