**Area of Isosceles Triangle**

One of the types of Triangle is Isosceles Triangle. There are several Formulas, Equations, and Theorems that are related to Area of Isosceles Triangle. if you are looking for the formulas to find the **Area of Isosceles Triangle** then you must take a look over here.

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**Area of Isosceles Triangle**

An isosceles triangle is a triangle with 2 sides of equal length and 2 equal internal angles adjacent to each equal side. Unlike an equilateral triangle wherein we can use any vertex to find out the altitude, in an isosceles triangle we are suggested to draw a perpendicular from the vertex which is common to the equal sides.

Let us see how to calculate the **Area Formula Of Isosceles Triangle**, altitude, and perimeter of an isosceles triangle.

From figure, let;

**a** be the measure of the equal sides of an isosceles triangle.

**b** be the base of the isosceles triangle.

**h** be the altitude of the isosceles triangle.

The Isosceles Triangle Formulas are,

*Area Of Isosceles Triangle = ½ bh*

*Area And Perimeter Of Isosceles Triangle = 2a+b*

*Altitude of an Isosceles Triangle = √a ^{2}– (b^{2}/4)*

Know Here With Example: __How To Find Area Of Right Angled Triangle?__

**Problems based on Isosceles Triangle**

**Question 1: ** How To Find The Area Of An Isosceles Triangle, altitude and perimeter of an isosceles triangle given a = 5 cm ; b = 9 cm?

**Solution:**

Given,

a = 5 cm

b = 9 cm

Perimeter of an isosceles triangle

= 2a + b

= 2(5) + 9 cm

= 10 + 9 cm

= 19 cm

Altitude of an isosceles triangle

= √*a2–(b ^{2}/4)*

=√25-(81/4)

=√25-20.25

= *2.179*

Formula For Area Of Isosceles Triangle

½ B*H

=½(5*9)

=45/2

=22.5 cm^{2}

**Question 2**: What Is The Area Of An Isosceles Triangle, altitude and perimeter of an given a = 12 cm ; b = 7 cm ?

**Solution**:

Given,

a = 12 cm

b = 7 cm

Perimeter of an isosceles triangle

= 2a + b

= 2(12) + 7 cm

= 24 + 7 cm

= 31 cm

Altitude of an isosceles triangle

= √*a ^{2}−b^{2/}4*

= √*144−12.25* cm

= √*131.75* cm

= 11.478 cm

Area Of Isosceles Triangle Given Two Equal Sides

= ½ *b×h*

= *7×11.4782* cm²

= *80.3462* cm²

= 40.173 cm²

Get Maths Vedic/Basic Formulas Free List: __Maths Formulas__

**Equation of Isosceles Triangle**

__Equation of Area Of Isosceles Trangle Formula__:

** Isosceles Triangle: **Two sides have equal length and Two angles are equal

**Isosceles Triangle Equations**

Where,

P=Perimeter

s=Semiperimeter

a=Length of side a

b=Length of side b

c=Length of side c

h=Altitude

m=Median

A=Angle A

B=Angle B

C=Angle C

t=Angle bisector

R=Circumscribed Circle Radius

r=Inscribed Circle Radius

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**Theorem of Isosceles Triangle**

In an isosceles triangle, the angles opposite to the equal sides are equal. Conversely, if the base angles of a triangle are equal, then the triangle is isosceles.

Get Here Formula To Calculate: __Surface Area Of Cone__

**Area Of Isosceles Triangle Using Heron’s Formula**

A method for calculating the area of a triangle when you know the lengths of all three sides

Let a,b,c be the lengths of the sides of a triangle. The area is given by:

Area =√ p( p−a) (p−b) (p−c)

where p is half the perimeter, or ((a+b+c) / 2)

**Area Of Isosceles Triangle With Angle And Side**

Area of a triangle – “side angle side” (SAS) method V

Area = (AB SinC) / 2

where a,b are the two known sides and C is the included angle.

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