# TOPIC 2: AREA AND PERIMETER ~ MATHEMATICS FORM 4

**TOPIC 2: AREA AND PERIMETER ~ MATHEMATICS FORM 4**

**Area of any Triangle**

The Formula for the Area of any Triangle

Derive the formula for the area of any triangle

Area of triangle is given by½bh, whereby b is the base of the triangle and h is the height of the given triangle. Consider the illustrations below:

From the figure above, we see where the base and height are located.

Applying the Formula to find the Area of any Triangle

Apply the formula to find the area of any triangle

Example 1

The base of a triangle is 12cm long. If the corresponding height is 7cm, find the area of the triangle.

Solution

Consider the figure below:

The area of a triangle is given by½bh.

Area =½×12cm×7cm

Area = 42cm

^{2}Therefore area of a triangle is 42cm

^{2}Example 2

The lengths of two sides of a triangle are 6cm and 8cm. Find the area of a triangle if the included is

Solution:

Consider the triangle below, name it triangle ABC.

The area of a triangle above is given by½b×h

So, Area = ½× 8cm× 6cm × sin 45°

=24cm

^{2}× sin45°= 16.97cm

^{2}Therefore the area of ABC = 16.97cm

^{2}

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