# Measurement: Finding the Area of a Triangle

*What is the formula to calculate the area of a triangle?*

*What is the formula to calculate the area of a triangle?*

Take the rectangle ABCD below.

Thearea of the rectangle = length × width

Cut the rectangle into 2.

Now, each half is a right-angled triangle.

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

Area of right-angled triangle = 1

2of area of rectangle = 1

2× length × width) = 1

2× base × height

Study the following examples.

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

2of area of rectangle made by the base and height = 1

2× base × height

The area of a triangle =1

2× base × height

Read also: Identifying the base and height of a triangle

*Calculating the area of triangles using formula*

*Calculating the area of triangles using formula*

Example 1:

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× base × height = 1

2× 3 cm × 6 cm = 9 cm^{2}

Example 2:

Find the area of the shaded pentagon below.

Area of triangle ABC = 1

2× (1.5 cm + 2 cm + 1.5 cm) × 4 cm = 1

2× 5 cm × 4 cm = 10 cm ^{2}

Area of triangle BED = 1

2× 1.5 cm × 1 cm = 0.75 cm ^{2}

Area of triangle GFC = 1

2× 1.5 cm × 3 cm = 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}