Area Of A Triangle

By Author: Adarsh Kumar
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Area of a Triangle
A plane figure with three straight sides and three angles. We know that a triangle is a closed shape and has three sides and three vertices. The basic formula of the area of a triangle i.e., A = ½*b*h.
The formula of the area of a triangle applies to every type of triangle acute, right, scalene, isosceles, equilateral, and obtuse. We should remember that the base and the height of the triangle are perpendicular to each other.
We are going to learn in this lesson about the area of a triangle and the different types of triangles.
What are triangles?
A triangle is a plane figure bounded by three straight lines. The straight lines AB, BC, and CA which bound triangles ABC are called its sides. The side BC may be regarded as the base and AD as the height.

Example. Find the area of a triangle with a base b=5cm and the height h= 6
Solution: The formula of the area of the triangle.
A = ½*b*h
= ½ *5*6
=30/2
=15cm²

Types of triangles: There are six types of triangles

Area of Triangle using ...
... Herons Formula
This formula is used when all three sides of the triangle are given.

Area = √s(s-a)(s-b)(s- c) where s= a+b+c/2

There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig. 12.10 ). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Solution:
Given the sides of the wall 15m, 11m, and 6m.
S = (15+11+6)/2 = 16m²
Using Heron’s formula,
Area of the message =

= √ [16(16-15) (16-11) (16-6)
= √ [16×1×5×10] m² = √800 m²
= 20√2 m²

There are types of areas of the triangle
Area of a right-angled triangle.
Area of an Equilateral Triangle.
Area of an Isosceles Triangle.

Area of a Right-Angled Triangle
A right-angled triangle is also known as the right triangle. It has one of the angles as 90 degrees. The height of the triangle is the length of the perpendicular side.

Area of an Equilateral Triangle
An area of an Equilateral Triangle is a triangle in which all sides are equal.

Area of an Isosceles Triangle
An area of an isosceles triangle has two of its sides equal and also the opposite the equal sides are equal.

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