Areas
Squares, Rectangles and Triangles

For a square, the area is given by x × x = x2 and the perimeter by 4x, where x is the length of a side.

For a rectangle, the area is given by lw and the perimeter by 2(l + w), where l is the length and w the width.

For a triangle, the area is given by bh and the perimeter by a + b + c, where b is the length of the base, h the height and a and c are the lengths of the other two sides.

Worked Examples

1

Find the area of each triangle below.

Use Area = bh or × base × height.

(a)
Show me
Area = × 5 × 4.2
= 10.5 cm²
(b)
Show me
Area = × 6 × 5.5
= 16.5 cm²
2

Find the perimeter and area of each shape below.

(a)
Show me

The perimeter is found by adding the lengths of all the sides.

P = 6 + 8 + 1 + 4 + 4 + 4 + 1 + 8
= 36 cm

To find the area, consider the shape split into a rectangle and a square.

Area = Area of rectangle + Area of square
= 6 × 8 + 42
= 48 + 16
= 64 cm²
(b)
Show me

Adding the lengths of the sides gives

P = 10 + 7 + 8 + 2 + 2 + 5
= 34 cm

The area can be found by considering the shape to be a rectangle with a square removed from it.

Area of shape = Area of rectangle − Area of square
= 7 × 10 − 22
= 70 − 4
= 66 cm²

Exercises

Find the area of each triangle.

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

Find the area of each shape.

(a)
cm²
(b)
cm²
(c)
cm²
(d)
cm²

The diagram shows the end wall of a shed built out of concrete bricks.

(a)

Find the area of the wall.

cm²
(b)

The blocks are 45 cm by 23 cm in size.

How many blocks would be needed to build the wall? (The blocks can be cut.)

blocks

The shaded area on the speed time graph represents the distance travelled by a bicycle.

Find the distance.

m

The diagram shows the two sails from a small sailing boat.

Find their combined area.

m²

Find the area of the arrow shown in the diagram.

cm²

The diagram shows how the material required for one side of a tent is cut out.

(a)

Find the area of the material shown if b = 3.2 m, c = 2 m and

(i)
a = 1.5 m m²
(ii)
a = 2 m m²
(b)

Find the area if a = 1.6 m, b = 3.4 m and c = 2 m.

m²

The shape above is shaded on centimetre squared paper.

(a)
Find the perimeter of this shape. cm
(b)
Find the area of this shape. cm²