Learn Triangles Area

Introduction to learning area of triangles

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted as `Delta ABC`. (Source: From Wikipedia).

Types of triangles

Equilateral triangles (3 equal sides and angles).
Isosceles triangles (Two equal sides and angles)
.Scalene triangles (No equal sides and angles).
Right triangles (Special case - any triangle with right angle).
Here, we are going to learn how to find the areas of triangles.


Learning formulas for finding the area of triangles


Here we are going to learn basic arithmetic formulas to find the area of different types of triangles.

Area of equilateral triangles
The area of an equilateral triangle can be found by using the formula,

A = `sqrt(3)/4` s2 square units, s - side of the triangle

Area of isosceles triangles
The area of an isosceles triangle can be found by using the formula,

A = `1/2` bh square units, b and h are base and height of the triangle respectively.

Area of scalene triangles
The area of a scalene triangle can be found by using the formula,

A = `sqrt(s(s-a)(s-b)(s-c))` square units

s = `(a + b + c)/2`. a, b, and c are the sides of the triangle


Example problems for finding the area of triangles


Here we are going to learn how to find the area of a triangle.

Example 1

Find the area of a triangle whose sides are equal to 16 cm.

Solution

Area of equilateral triangle = `sqrt(3)/4` s2

= `sqrt(3)/4` * 16 * 16

= `sqrt(3)` * 4 * 16

= `64sqrt(3)`

So the area of the given triangle is `64sqrt(3)` square cm.

Example 2

Find the area of a triangle with height 5 cm and base 4 cm.

Solution

Area = `1/2` bh square units

= `1/2` * 4 * 5

= 10

So, the area of the given triangle is 10 square cm.

Example 3

Find the area of a triangle with sides, 2 ft, 5 ft, and 6 ft.

Solution

Area of a scalene triangle = `sqrt(s(s-a)(s-b)(s-c))`

s = `(a + b + c)/2`

s = `(2 + 5 + 6)/2`

= `13/2`

= 6.5

Area = `sqrt(6.5(6.5-2)(6.5-5)(6.5-6))`

= `sqrt((6.5)(3.5)(1.5)(0.5))`

= `sqrt(17.0625)`

= 4.13

So the area of the given triangle is 4.13 square ft.