Triangles

Shape and Space

Area of a right-angled triangle

What proportion of this rectangle has been shaded?

8 cm

4 cm

What is the shape of the shaded part?

What is the area of this right-angled triangle?

Area of the triangle = × 8 × 4 = 12

4 × 4 = 16 cm2

We can use a formula to find the area of a right-angled triangle:

Area of a right-angled triangle

base, b

height, h

Area of a triangle = 12

× base × height

= 12bh

Area of a right-angled triangle

Calculate the area of this right-angled triangle.

6 cm

8 cm

10 cm

To work out the area of this triangle we only need the length of the base and the height.

We can ignore the third length opposite the right angle.

Area = 12

× base × height

= × 8 × 612

= 24 cm2

Area of a triangle

What proportion of this rectangle has been shaded?

8 cm

4 cm

Drawing a line here might help.

What is the area of this triangle?

Area of the triangle = × 8 × 4 = 12

4 × 4 = 16 cm2

Area of a triangle

The area of any triangle can be found using the formula:

Area of a triangle = × base × perpendicular height12

base

perpendicular height

Or using letter symbols,

Area of a triangle = bh12

Any side of the triangle can be taken as the base, as long as the height is perpendicular to it:

The area of a triangle

b

h

bh b

h

Area of a triangle

What is the area of this triangle?

Area of a triangle = bh12

7 cm

6 cm

= 12

× 7 × 6

= 21 cm2

Area of a triangle

The area of a triangle