# Area Of Triangle

*If you fold a square piece of paper diagonally (from corner to corner) in half, it makes a triangle.*

*If you fold a rectangular piece of paper diagonally in half, it makes another triangle.*

*Therefore, the rule for the Area of a Rectangle and the Area of a Triangle are related.*

Area of Triangle = | B × H |

2 |

where
**B** is the base
**H** is the perpendicular height (at right angles to the base).

All 3 triangles above have the same base, the same perpendicular height and therefore, all 3 triangles have the same area.

## Example - Painting a Roof Gable

In this diagram of a roof gable at the front of a house, what is the area to be painted? (Include the window so there's paint left over.)

**Answer:**

Area of triangle

= (B × H) ÷ 2

= 10 × 2.5

= 25 m^{2}

## Maths Fun - Heron's Formula

Though more complex, this is a useful rule in real life because **we only need to know the lengths of the 3 sides of any shaped triangle** to find the area.

The sides are called **a**, **b**, and **c**.

Heron's rule has 2 parts:

S = | (a + b + c) |

2 |

Area of triangle = √S ( S – a) (S – b) (S – c)

What is the area of a triangular city park whose **sides are 100 metres, 150 metres and 200 metres**?