## Finding the Area of a Triangle

#### Formula for Area of a Triangle

**The area of a triangle =**

× base × height

1 |

2 |

#### 1. Deriving the formula to calculate area of a triangle.

In the figure below,

Cut the rectangle into 2.

Now, each half is a right-angled triangle.

And, each right-angled triangle, therefore, has half the area of the rectangle.

Area of right-angled triangle

=

area of rectangle

=

× (length × width)

=

× (base × height)

**Area of the rectangle ABCD = length × width**Cut the rectangle into 2.

Now, each half is a right-angled triangle.

And, each right-angled triangle, therefore, has half the area of the rectangle.

Area of right-angled triangle

=

1 |

2 |

=

1 |

2 |

=

1 |

2 |

Study the following examples.

In both examples above, the area of the triangle is

So,

Area of a triangle

=

of area of rectangle made by the base and height

=

× (base × height)

In both examples above, the area of the triangle is

**half the area of the rectangle made by the base and height**.So,

Area of a triangle

=

1 |

2 |

=

1 |

2 |

#### 2. Find the area of a triangle that has a base of 3 cm and a height of 6 cm.

Both triangles above have a base of 3 cm and a height of 6 cm.

Therefore, they both have the same area which is calculated as below:

Area of triangle

=

1 |

2 |

=

1 |

2 |

=

**9 cm**

^{2}#### 3. Find the area of the shaded pentagon below.

Area of triangle ABC

=

1 |

2 |

=

1 |

2 |

= 10 cm

^{2}

Area of triangle BED

=

1 |

2 |

= 0.75 cm

^{2}

Area of triangle GFC

=

1 |

2 |

= 2.25 cm

^{2}

**Area of pentagon ADEFG**

= Area (ABC) − Area (BED) − Area (GFC)

= 10 cm

^{2}− 0.75 cm

^{2}− 2.25 cm

^{2}

=

**7 cm**

^{2}