Area
3.0 Measurements · 3.2 Area
Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 3.0 Measurements | Sub-Strand 3.2 Area (10 lessons)
Lesson objectives
By the end of this sub-strand, you should be able to:
- Calculate the area of circles and of a sector of a circle
- Work out the surface area of cubes, cuboids, cylinders, and triangular prisms
- Work out the area of irregular shapes using square grids
Area
Area measures the flat space a shape covers. Painting a wall, tiling a floor and buying material to wrap a box all need it.
Every answer is in square units, such as cm² or m². If your answer is in cm, you have found a length, not an area.
a) Area of a circle
The rule is A = πr². Square the radius first, then multiply by π.
Watch the difference from circumference. Circumference uses 2πr and gives a length. Area uses πr² and gives a square measure. Mixing them is the commonest error here.
If the question gives the diameter, halve it before squaring.
b) Area of a sector
A sector is a fraction of the circle. Its area is that same fraction of the circle's area.
The fraction is the angle at the centre divided by 360, exactly as it was for arc length.
c) Surface area of a solid
Surface area is the total area of all the faces. Think of unfolding the solid flat and measuring every piece.
A cuboid has six faces in three matching pairs. Work out one of each pair, add them, then double.
A cube is simpler still. All six faces are identical, so the surface area is 6 × side × side.
d) Cylinders and prisms
A cylinder unrolls into two circles and one rectangle. The rectangle's length is the circumference of the circle, so its area is 2πr × h.
Surface area of a cylinder = 2πr² + 2πrh.
A triangular prism has two triangular ends and three rectangular sides. Work out the two triangles, then each rectangle, and add them all.
The safest method for any prism is to sketch its net first. Nothing gets forgotten when you can see every face.
e) Irregular shapes on a grid
Some shapes have no formula. Put them on a square grid and count.
Count every square that is fully inside the shape.
Then count the part-squares. Take any that is half or more as a whole square, and ignore any less than half.
Add the two counts. The answer is an estimate, and a finer grid gives a better one.
This is how a map reader estimates the area of a lake or a farm plot.
f) Where this is used
A painter works out how much paint a room needs. A farmer measures a field before ordering seed. A packaging designer calculates the card required for a box.
Words to know
- Surface area -- the total area of all the faces of a solid shape added together.
- Sector -- a portion of a circle bounded by an arc and two radii; its area is a fraction of the full circle's area.
:::checkpoint Check yourself
- Find the area of a circle of radius 14 cm, taking π as 22/7.
- Find the area of a 90° sector of that circle.
- Find the surface area of a cuboid measuring 10 cm by 4 cm by 3 cm.
- On a grid, how do you treat a square that is exactly half covered? :::
Bridge to practice
Try the exercises below -- on the area of circles and sectors, and the surface area of cubes, cuboids, cylinders, and triangular prisms.