Online Tution   »   Important Question   »   Area of a Triangle: Formula, Solved...

Area of Triangle: Formula in Co-ordinate Geometry

Area of Triangle

The region enclosed by the three sides of any triangle is defined as the area of a triangle. In general, it is equal to half of the base times the height, i.e. A = 1/2 (bxh). As a result, in order to calculate the area of a triangular polygon, we must first find the base (b) and height (h). It is applicable to all forms of triangles, including scalene, isosceles, and equilateral triangles. It should be observed that the triangle’s base and height are perpendicular to each other. The area unit is measured in square units (m2, cm2). In this article, we have discussed the area of the triangle, methods to calculate the area of the triangle. Stay tuned and read the entire article to learn how to calculate the area of a triangle and bookmark this page to get the latest updates of all the articles. 

Read More About:

Area of a Triangle: Formula in Co-ordinate Geometry_40.1

 

Area of Triangle Formula with 3 sides

There are many ways to calculate the formula of a Triangle. For example, When we know two sides and the angle between them, we can use trigonometric functions to calculate the area of a triangle. The other method we can apply when we know the lengths of all three sides of a triangle, we can apply Heron’s formula to compute the area of a triangle. Furthermore, the basic formula for calculating the area of a triangle is:

Area of a Triangle = A = ½ (b × h) square units

Here A = Area of Triangle

B = Base of Triangle 

H = Height of a Triangle

 

Area of a Triangle in Co-ordinate Geometry

Here we have given the methods to calculate the Area of a Triangle using formulas. The formulas to calculate the area of different types of triangles like an isosceles triangle, equilateral triangle, and right-angled triangle are given below.

Area of an Isosceles Triangle

Two of the sides of an isosceles triangle are equal, and the angles opposite the equal sides are likewise equal.

Area of an Isosceles Triangle = 1/4 b√(4a2 – b2)

Where,  b = Base of a Triangle 

a = Measure of one of the sides from two equal sides

Area of a Right-Angled Triangle

A right-angled triangle, often known as a right triangle, has one 90° angle and two 60° angles that add up to 90°. As a result, the height of the triangle is equal to the length of the perpendicular side.

Area of a Right Triangle = A = 1/2 × Base × Height

Here A = Area of Triangle

B = Base of Triangle 

H = Height of a Triangle

Area of an Equilateral Triangle

An equilateral triangle is one with all of its sides equal. The perpendicular traced from the triangle’s vertex to its base divides the base into two equal pieces. To compute the area of an equilateral triangle, we must first determine the length of its sides.

Area of an Equilateral Triangle = A = (√3)/4 × side2

Here, A = Area of Triangle

Side = side of the triangle

 

Area of a Triangle Formula: Summary 

Below we have given the formulas to calculate the area of a triangle. Check out the table below: 

Particulars Area of Triangle Formula
When a triangle’s base and height are known.  A = 1/2 (base × height)
When all the sides of a triangle are given like a, b, and c. Heron’s formula

Area of a scalene triangle = 

√s(s−a)(s−b)(s−c)

 s = (a + b + c)/2

Where,  a, b, and c = sides 

S = semi-perimeter of triangle

When an angle and two sides of a triangle are given  A = 1/2 × side 1 × side 2 × sin(θ)

Where, θ = Angle between the given two sides

When the height and base of the triangle are given. Area of a right-angled triangle = 1/2 × Base × Height
In the case of an equilateral triangle  Area of an equilateral triangle = (√3)/4 × side2
In the case of an isosceles triangle  Area of an isosceles triangle = 1/4 b√(4a2 – b2)

Where,  b = base of the triangle the length of an equal side.

 

 

Area of Triangle: Solved Examples and Formula

Q.1: Find the area of a triangle with a base of 20 cm and a height of 10 cm.

Area of triangle = (1/2) × b × h
A = 1/2 × 20 × 10
A = 1/2 × 200

Thus, the area of a triangle is 100 cm2.

Q.2: Find the area of a triangle with a base of 6 cm and a height of 3 cm.

Area of triangle = (1/2) × b × h
A = 1/2 × 6×3

A = 1/2 ×18

Thus, the area of a triangle is 9 cm2.

Q.3: Find the area of a triangle with a base of 12 cm and a height of 16 cm.

Area of triangle = (1/2) × b × h
A = 1/2 × 12 × 16
A = 96

Thus, the area of triangle is 96 cm2.

Q.4: Find the area of an equilateral triangle with a side of 12 cm.

Area of an Equilateral Triangle = A = (√3)/4 × (side)2

Given the side of equilateral triangle = 12cm

A = (√3)/4 × (side)2

A = (√3)/4 × (12)2

A = (√3)/4 × 144

A = 36√3 cm2

Read More About:

Area of a Triangle: FAQs

Q. How to calculate the area of an equilateral triangle?

Area of an Equilateral Triangle = A = (√3)/4 × (side)2

Q. How to calculate the area of a right-angled triangle?

Area of right-angle triangle = (1/2) × b × h

Q. What is Heron’s formula in Triangle?

Heron’s formula 

Area of a scalene triangle = √s(s−a)(s−b)(s−c)

 s = (a + b + c)/2

Where,  a, b, and c = sides 

S = semi-perimeter of triangle

Q. How to calculate the area of the Isosceles Triangle?

Area of an Isosceles Triangle = 1/4 b√(4a2 – b2)

 

 

 

 

 

 

Sharing is caring!

Thank You, Your details have been submitted we will get back to you.
Was this page helpful?

Leave a comment

Your email address will not be published. Required fields are marked *