How to Find the Area of a Triangle

In a two-dimensional plane, the area of a triangle is described as the amount space filled by its three sides. The area of a triangle is the half the products of its base and height, orA=12 ×b×h. This formula works for any triangle, whether it’s a scalene triangle, an isosceles triangle, or an equilateral triangle. It’s important to remember that a triangle’s base and height are normal  to each other.

Area of a Triangle

The area of a triangle changes based on the length of the sides and internal angles of the triangle. The area of a triangle is measured in square units such as metres, centimetres, and inches.

Area of a Triangle Formula

Several formulas can be used to compute the area of a triangle. Once we recognise two sides and the angle formed between them, we can use trigonometric functions to find the area of a triangle. However, the following is the basic formula for calculating the area of a triangle:

 A=12 ×b×h 

Here b is the base of triangle and h is the height of triangle.

Example

Calculate the area of a triangle having a base of 2 cm and a height of 4 cm.

Solution: The area of a triangle is calculated as  A=12 ×b×h 

Here a=2 cm and h=4cm

 A=12 ×2×4

 A=4cm2.

Triangles are characterised as acute, obtuse, or right triangles based on their angles. When classed by their sides, they can be scalene, isosceles, or equilateral triangles.

Area of triangle using Heron’s formula

Heron’s method is used to determine the area of a triangle when the lengths of its three sides are determined. To use this method, we must first get the triangle’s perimeter, which is the distance covered around the triangle and is determined by summing the lengths of all three sides. There are two crucial steps in Heron’s formula.

Step 1: To calculate the semi perimeter, combine all three parts of the triangle and divide by two (half perimeter).

Step 2: Fill in the quantity of the triangle’s semi-perimeter in the fundamental formula, ‘Heron’s Formula.’

 s=(a+b+c)/2

 Area of  Triangle will be given as= ss-a(s-b)(s-c)

We can also find the semi perimeter by applying following formula

s=(a+b+c)/2

How to find the area of a triangle?

Depending on the type of triangle and the specified measurements, the area of a triangle can be determined using a variety of formulas.

The formulas for the area of triangles for all types of triangles, including equilateral, right-angled, and isosceles triangles, are listed here.

Area of Right angled Triangle

A right-angled triangle, often known as a right triangle, has one angle of 90 degrees and two acute angles that add up to 90 degrees. As a result, the triangle’s height equals the length of the normal side. So Area will be given as: Area=12 ×Base ×Height.

Area of an Equilateral Triangle

A triangle with all sides equal is called an equilateral triangle. The base is divided into two equal portions by the normal traced from the triangle’s vertices to the base. To compute the area of an equilateral triangle, we must first determine its side measurements.

 Area=(3)×Side2 /4

Area of an Isosceles Triangle

The angles opposing the equal sides are also equal in an isosceles triangle.

 Area of an isosceles=14 b4a2–b2

Area of a Triangle Solved Examples

Calculate the area of a triangle whose two sides are 12 and 11 cm and perimeter is 36cm.

Solution:

Given perimeter =36cm here a=12 cm and b=11 cm

Then third side c=36-12+11=13cm

So 2s=36cm s=362=18cm

 s-a=18-12=6cm

 s-b=18-11=7cm

 s-c=18-13=5cm

As we know , Area=ss-a(s-b)(s-c)

Hence Area= 18×6×7×5

 Area=6105 cm2

Conclusion

The space occupied by a two-dimensional shape is its area. The area of a pattern can be calculated by splitting it into unit squares and counting the number of unit squares in the form; each unit square occupies one square unit of space. The whole length of the boundary defines a polygon’s perimeter. We can find the lengths of a triangle’s three sides by adding them together. The perimeter of a triangle can be used to calculate the length of fence necessary for a triangular park.  When we know the lengths of all three sides of a triangle, we can apply Heron’s formula to compute its area.