Units of Measurement 3
Estimating Areas

A square with sides of 1 cm has an area of 1 cm2 .

Worked Examples

1

Find the area of the shaded shape.

Show me The shape covers 11 squares, so its area is 11 cm2 .
2

Find the area of the shaded triangle.

Show me

The triangle covers 6 full squares marked F,

and 4 half squares marked H.

Area = 6 + 2
= 8cm2
3

Estimate the area of the shape shaded in the diagram.

Show me

This is a much more complicated problem as there are only 9 full squares marked F, but many other part squares. You need to combine part squares that approximately make a whole square. For example,

the squares marked * make about 1 full square;

the squares marked × make about 1 full square;

the squares marked + make about 1 full square;

the squares marked • make about 1 full square.

Thus the total area is approximately

9 + 4 = 13 cm2

Challenge!

Use 12 matchsticks to form 6 equilateral triangles, all of the same area. Move only 4 matchticks from your figure so as to get 3 equilateral triangles, 2 of which are of the same area.

Exercises

Find the area of each of the following shapes.

(a)
cm²
(b)
cm²
(c)
cm²
(d)
cm²
(e)
cm²
(f)
cm²

By counting the number of whole squares and half squares, find the area of each of the following shapes.

(a)
cm²
(b)
cm²
(c)
cm²
(d)
cm²
(e)
cm²
(f)
cm²

The diagrams below shows the outlines of two islands, A and B. The grid squares have sides of length 1 km. Find the approximate area of each island.

(a)
km²
(b)
km²

Each of the squares in this grid has an area of 1 square centimetre.

Work out the area of the shaded shape.

Area = cm²

Investigation

Which of the following shaded figures has the greatest area? The squares are of the same length and the curved lines are all arcs of circles.