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Area and Perimeter of Different Types of Triangle with Example

 What is the Area of the Triangle?

The region enclosed by three sides of the triangle is known as the area of a triangle. It is denoted by the capital letter A and its SI unit is meter Squared(m2). The area of the triangle is equal to half of the product of the base and its height. The area is a two-dimensional quantity.
Area of triangle = (1/2)*Base*Height
it means to calculate the total area enclosed by three sides of the triangle, its required base, and the height of the triangle.it is applicable to all types of triangles. In this post, we will see the basic formula for all types of triangles.
area of traingle
A =\frac{1}{2}\times Base\times Height

Example: Find the area of a triangle If the Base of the triangle is 100 m long and its height is 40 m.long.

From Question
Height =H = 40 m
Base = B= 100 m
Let area of triangle = A, then By Formula 
A =\frac{1}{2}\times Base\times Height
A =\frac{1}{2}\times 100\times 40=2000\ m^{2}
Hence the area of the triangle = is 2000 meters Square

Area of Scalene Triangle

In Scalene Triangle all three sides are unequal. Hence the area of the Scalene triangle is Calculated by heron's formula. According to heron's formula Area of the Triangle is given as
A =\sqrt{S(S-a)(S-b)(S-c)}
where S is semi perimeter of the triangle and it is given as 
S =\frac{1}{2}(a+b+c)
Where a,b, and c are the lengths of sides of the triangle. In Triangle Whose vertices are denoted by A, B and C then the side of the triangle in front of Vertex A is denoted by a, and so on. As shown in the figure given below.
heron formula

Perimeter  and  Perimeter Formula of Triangle

The total boundary length of a given polygon is called the perimeter of the polygon.it means that sum of the length of all three sides of the triangle is called the perimeter of the triangle. if the length of the sides of the triangle is a,b and c then its perimeter will be given as 
S =a+b+c

Example:10 m,12 m, and 8 m are sides of a scalene Triangle. Calculate its area and Perimeter.

Sides of triangle are a= 10 m,b =12 m and c =8 m
Let S is the Perimeter of the Triangle then by the formula 
S =a+b+c
S =10+12+8 = 30 m
The perimeter of the Triangle is 30 m
Semi Perimeter of the Triangle Will be 30/2 =15 m
Let A is the total area of the triangle then by Heron's formula 
A =\sqrt{S(S-a)(S-b)(S-c)}
A =\sqrt{15(15-10)(15-12)(15-8)}
A =\sqrt{15(5)(3)(7)}=15\sqrt{7}\ m^{2}
A =\sqrt{15(5)(3)(7)}=15\sqrt{7}\ m^{2}
A =15\sqrt{7}\ m^{2}

Area of Equilateral Triangle

In the Equilateral triangle, all three sides of the triangle are equal in length. Let the length of equal sides of the triangle is a then the area enclosed by the Equilateral triangle is given as 
A =\frac{\sqrt{3}}{4}a^{2}

Example: If the length of the side of an Equilateral triangle is 10 cm then Calculate its area A and perimeter S of the triangle.

Given that
Length of Side of Equilateral Triangle = 10 cm
Let A is the area of the Triangle Then By  Formula 
A =\frac{\sqrt{3}}{4}a^{2}
A =\frac{\sqrt{3}}{4}(10)^{2} =\frac{\sqrt{3}}{4}\times100=25\sqrt{3}\ cm^{2}
Let S is the perimeter of the Triangle then By Definition of Perimeter.
S = Sum of Length of All three Sides of Triangle
S = a+b+c
S = 10+10+10=30 cm
S =30 cm

Area of Isosceles Triangle

In the Isosceles triangle, any two sides of the triangle are equal in length. If the equal  length of the triangle is a and height of the triangle is H then the area enclosed by the Isosceles triangle is given as
isosceles triangle
A =\frac{1}{2}\times Base\times Height

Example: The height of a triangle is 10 cm and two other sides of the triangle are equal in length by 20 cm.

Given that
 Height of triangle = H =10 cm
Length of Base = B = 20 cm 
Let A is the area of the Isosceles Triangle then By Formula 
A =\frac{1}{2}\times Base\times Height
A =\frac{1}{2}\times20\times 10 =100\ m^{2}
Mathematics
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