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How to Find the Area of an Isosceles Triangle? Formulas, Equations, Theorems

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.

Here on this page of recruitmentresult.com we have given all the details about Area of an Isosceles Triangle including Formulas, Equations, Theorems etc.

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.

Area of 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 = √a2– (b2/4)

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–(b2/4)

=√25-(81/4)

=√25-20.25

2.179

Formula For Area Of Isosceles Triangle
½ B*H

=½(5*9)

=45/2

=22.5 cm2

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
= √a2−b2/4

= √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:

Equation of Isosceles Triangle

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

Isosceles Triangle Equations

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

Get Easiest Methods: Ways to Improve Math Skills

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.

Theorem of Isosceles Triangle

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.

We hope with the help of details given here on this page it will become easier for you all to understand the concept of Area of an Isosceles Triangle and its formulas. To get more related updates keep visiting our pages.

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