1. Triangles Shape and Space

2. 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 = 1 2 4 × 4= 16 cm 2

3. 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 = 1 2 × base × height = 1 2 bh

4. 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 = 1 2 × base × height = × 8 × 6 1 2 = 24 cm 2

5. 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 = 1 2 4 × 4= 16 cm 2

6. Area of a triangle The area of any triangle can be found using the formula: Area of a triangle = × base × perpendicular height 1 2 base perpendicular height Or using letter symbols, Area of a triangle = bh 1 2

7. 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 b h b h

8. Area of a triangle What is the area of this triangle? Area of a triangle = bh 1 2 7 cm 6 cm = 1 2 × 7 × 6 = 21 cm 2

9. Area of a triangle

10. The area of a triangle