# How to find the area of a triangle with examples.

The area of a triangle is half the product of the base and the height of the triangle. A triangle is a three-sided plane figure. The area of a triangle is the total space occupied by the three sides of the triangle in a 2-dimensional shape. In this article, we will discuss the area of a triangle in detail.

## What is the area of a triangle

The area of a triangle refers to the total space occupied by the three sides of a triangle in a 2- dimensional shape. The formula for finding the area of a triangle is half the product of the perpendicular height and the base of the triangle. i.e 1/2 × base × height. Note that any side of the triangle can be the base. The perpendicular

## How to find the area of a triangle.

To find the area of a triangle, follow the simple steps below.

• make sure the unit of measurement of the sides is the same.

• multiply the base and the perpendicular height of the triangle.

• multiply the product of the base and the height by half (1/2).

• simplify to find the area of the triangle. Let’s understand better by working on some examples.

Example 1. Find the area of the triangle whose base is 6cm and height is 7cm.

Solution

The area of a triangle is = **(1/2) × base × height**

Considering the triangle above, the base = 6cm and the height = 7cm.

Now, the area of the triangle is = (1/2) × 6cm × 7cm

= (1/2) × 42cm^{2}

= 21cm^{2}

Examples 2. What is the area of a triangle whose base is 8cm and height is 10cm?

Solution

The Area of a triangle is = **(1/2) × base × height**

where the base is 8cm and the height is 10cm.

= (1/2) × 8cm × 10cm

= (1/2) × 80cm^{2}

= 40cm^{2}

Example 3. If the area of a triangle is 22.5cm^{2} and the base is 5cm find the height.

Solution

Area of a triangle = **(1/2) × height × base **

Where the area of the triangle is = 22.5cm^{2}, the base is = 5cm and the height is = ?

Now, since we know the area of the triangle, we can find the height of that triangle by substituting the values. So, we know the area of a triangle is = **(1/2) × base × height (h)**

=> 22.5cm^{2} = (1/2) × 5cm × h

=> 2× 22.5cm^{2} = 5h, i.e multiplying both sides by 2 to clear the fraction.

=> 45cm^{2} = 5h, Divide both sides by 5

=> (45)/5 = (5h)/5

=> 9cm = h

Therefore, the height of the triangle is 9cm.

Read also:

• The perimeter of a triangle with examples here

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