To identify and calculate the area and perimeter of a triangle, we need to know the lengths of its sides and, in some cases, its base and height.
Step 1: Identify the Triangle
First, determine the type of triangle you are dealing with—whether it’s a scalene, isosceles, or equilateral triangle. You can do this by examining the lengths of the sides:
- Scalene: All sides are of different lengths.
- Isosceles: Two sides are of equal length.
- Equilateral: All three sides are of equal length.
Step 2: Calculate the Perimeter
The perimeter (P) of a triangle can be calculated using the formula:
P = a + b + c
where ‘a’, ‘b’, and ‘c’ are the lengths of the sides of the triangle.
Step 3: Calculate the Area
The area (A) can be calculated using different formulas based on the information available about the triangle:
- If you know the base (b) and height (h):
A = (1/2) × b × h - If you know all three sides (a, b, c), you can use Heron’s formula:
First, calculate the semi-perimeter (s):
s = (a + b + c) / 2
Then,
A = √(s × (s – a) × (s – b) × (s – c))
Example:
Consider a triangle with sides of lengths 3 cm, 4 cm, and 5 cm.
- Step 1: Identify the triangle. (This is a scalene triangle.)
- Step 2: Calculate the perimeter: P = 3 + 4 + 5 = 12 cm.
- Step 3: Calculate the area using Heron’s formula:
s = (3 + 4 + 5) / 2 = 6
A = √(6 × (6 – 3) × (6 – 4) × (6 – 5))
A = √(6 × 3 × 2 × 1) = √(36) = 6 cm².
Thus, for the given triangle, the area is 6 cm² and the perimeter is 12 cm.