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