Area
3.0 Measurements · 3.3 Area
Syllabus tag: Kenya CBC | Grade 7 Mathematics | Strand 3.0 Measurements | Sub-Strand 3.3 Area (8 lessons)
Lesson objectives
By the end of this topic, you will be able to:
- Identify the relationship between square metres (m²) and hectares as units of area
- Work out the area of a rectangle, parallelogram, rhombus and trapezium
- Work out the area of circles
- Calculate the area of borders and combined shapes
Area
Area measures the flat space inside a shape. Every answer is in square units, such as cm², m² or hectares.
a) Square metres and hectares
A hectare is the unit used for land. One hectare is 10 000 m², which is a square 100 m by 100 m.
A football pitch is roughly one hectare, which makes it a useful thing to picture.
To change m² to hectares, divide by 10 000. To go the other way, multiply.
b) Rectangle and parallelogram
A rectangle's area is length times width.
A parallelogram uses base times perpendicular height, not the slanting side.
The perpendicular height is the straight-up distance between the two parallel sides. Using the slanting side gives an answer that is too large.
c) Rhombus and trapezium
A rhombus has four equal sides and its diagonals cross at right angles. Its area is half the product of the diagonals.
A trapezium has one pair of parallel sides. Its area is the average of those two parallel sides, multiplied by the perpendicular height between them.
Write it as ½(a + b) × h, where a and b are the parallel sides.
Add the parallel sides before halving. Halving only one of them is a common error.
d) Area of a circle
The rule is A = πr². Square the radius first, then multiply by π.
Keep it apart from circumference. Circumference is 2πr and measures a length. Area is πr² and measures a surface.
e) Borders and combined shapes
A border is the strip between two shapes, such as a path round a garden.
Work out the area of the whole outer shape, then the area of the inner shape, and subtract.
For a combined shape, split it into parts you recognise, work out each, and add.
Sketch the split before calculating. Marking each piece on the sketch stops you counting a part twice or missing one.
f) Where this is used
A farmer buying seed for a field. A painter estimating paint. A tiler counting tiles. A landowner reading a title deed measured in hectares.
Words to know
- Area — the amount of surface a shape covers, measured in square units.
- Hectare (ha) — a unit of area equal to 10,000 m², used for land.
- Perpendicular height — the straight up-and-down distance between two sides, used in area formulas, distinct from a slanted side length.
- Border — a frame-like strip of area, found by subtracting an inner area from an outer one.
:::checkpoint Check yourself
- How many square metres are in one hectare?
- Find the area of a parallelogram with base 12 cm and perpendicular height 5 cm.
- Find the area of a trapezium with parallel sides 6 cm and 10 cm, and height 4 cm.
- Why must you use the perpendicular height, not the slanting side? :::
Bridge to practice
Try the exercises below — on area of rectangles, parallelograms, rhombuses, trapeziums, circles and combined shapes.