# Perimeter and Area of Triangle

The distance covered around a closed figure on a plane is called its perimeter.

### Perimeter of Triangle

If the sides of a triangle are a, b, c, then

Perimeter = a + b + c

Example 1: Find the perimeter of a triangle ABC, Where AB = 5 cm, BC = 7 cm and CA = 3 cm.

Perimeter of triangle ABC = AB + BC + CA

5 + 7 + 3 = 15 cm

Example 2: An equilateral triangle the side is 5 cm, find its perimeter.

All the sides of an equilateral triangle are equal. Hence, the perimeter of an equilateral triangle = Side + Side + Side or 3 × side.

= 3 × 5 = 15 cm

### Area of Triangle

Area of the triangle, Δ = 1/2 × Base × Corresponding height

Example 3: Find the area of a triangle whose base is 9 cm and height 6 cm.

Area of triangle = 1/2 × base × corresponding height

= 1/2 × 9 × 6 = 27 cm2

Example 4: Find the length of the base of ΔPQR, when its area is 30 cm2 and height is 6 cm.

1/2 × base × 6 = 30

base = 10 cm

### Heron's Formula

Sometimes, you are not given the altitude (height) corresponding to the given base of a triangle. Instead of that you are given the three sides of the triangle.

If the sides of a triangle are a, b, c, then

$$\Delta = \sqrt{s(s - a)(s - b)(s - c)}$$

2s = a + b + c

Example 5: Find the area of a triangle when the sides of triangle are 25 cm, 60 cm and 65 cm.

2s = 25 + 60 + 65 = 150 cm

s = 75 cm

$$\text{Area} = \sqrt{75(75 - 25)(75 - 60)(75 - 65)}$$

$$= \sqrt{75 \times 50 \times 15 \times 10}$$

= 750 cm2