Area of isosceles triangle formula with three sides .

Area of isosceles triangle formula with three sides.

Formula

Area Of Isosceles Triangle Formula

The area of an isosceles triangle is the amount of region enclosed by it in a two-dimensional space. The general formula for the area of triangle is equal to half the product of the base and height of the triangle.

Here, a detailed explanation about the area of isosceles triangle with three sides , its formula and derivation are given along with a few solved example questions to make it easier to have a deeper understanding of this concept.

 Area Isosceles triangle formula with three sides
Area of isosceles triangle formula with three sides .

Check more mathematics formulas here.

What is the Formula for Area of Isosceles Triangle?

What is area  isosceles triangle formula?

Area of  isosceles triangle with three sides is one which has at least two sides of equal length. This property is equivalent to two angles of the triangle being equal. An isosceles triangle has two equal sides and two equal angles area of isosceles formula with three sides

An isosceles triangle has two equal side lengths and two equal angles, the corners at which these sides meet the third side is symmetrical in shape

. If a perpendicular line is drawn from the point of intersection of two equal sides to the base of the unequal side, then two right-angle triangles are generated.

Area of Isosceles Triangle Formula with three sides

The area of an isosceles triangle is given by the following formula:

Area = ½ × base × Height

Also,

The perimeter of the isosceles triangle P = 2a + b
The altitude of the isosceles triangle h = √(a2 − b2/4)

 To Find Isosceles Triangle Area

Formulas to Find Area of Isosceles Triangle
Using base and Height A = ½ × b × h
Using all three sides A = ½[√(a2 − b⁄4) × b]
Using the length of 2 sides and an angle between them A = ½ × b × c × sin(α)
Using two angles and length between them A = [c2×sin(β)×sin(α)/ 2×sin(2π−α−β)]
Area formula for an isosceles right triangle A = ½ × a2

 Calculate Area  of an Isosceles Triangle with three sides ?

If the length of the equal sides and the length of the base of an isosceles triangle are known, then the height or altitude of the triangle is to be calculated using the following formula:

The Altitude of an Isosceles Triangle = √(a2 − b2/4)

Thus,

Area of Isosceles Triangle Using Only Sides = ½[√(a2 − b/4) × b]

Here,

  • b = base of the isosceles triangle
  • h = height of the isosceles triangle
  • a = length of the two equal sides

Derivation for Isosceles Triangle Area Using Heron’s Formula

The area of an isosceles triangle can be easily derived using Heron’s formula as explained below.

According to Heron’s formula,

Area = √[s(s−a)(s−b)(s−c)]

Where, s = ½(a + b + c)

 

Area = √[s(s−a)(s−b)(s−c)]

Or, triangle = b/2 × √(a2 − b2/4)

Area of Isosceles Right Triangle Formula

Formula for Isosceles Right Triangle Area= ½ × a2

Derivation:

 

Area = ½ ×base × height

area = ½ × a × a = a2/2

Perimeter of Isosceles Right Triangle Formula

P = a(2+√2)

Derivation:

The perimeter of an isosceles right triangle is the sum of all the sides of an isosceles right triangle.

Suppose the two equal sides are a. Using Pythagoras theorem the unequal side is found to be a√2.

Hence, perimeter of isosceles right triangle = a+a+a√2

 Area Isosceles triangle formula with three sides
Area of isosceles triangle formula with three sides

 

Area of Isosceles Triangle Using Trigonometry

Using Length of 2 Sides and Angle Between Them

A = ½ × b × c × sin(α)

Question 4Find the area, altitude and perimeter of an isosceles triangle given a = 12 cm, b = 7 cm.

Solution:

Given,

a = 12 cm

b = 7 cm

Perimeter of an isosceles triangle

 

²

Frequently Asked Questions

What is an Isosceles Triangle?

An isosceles triangle can be defined as a special type of triangle whose 2 sides are equal in measure. For an isosceles triangle, along with two sides, two angles are also equal in measure.

What does the Area of an Isosceles Triangle Mean?

The area of an isosceles triangle is defined as the amount of space occupied by the isosceles triangle in the two-dimensional plane.

What is the Formula for Area of Isosceles Triangle?

To calculate the area of an equilateral triangle, the following formula is used:

A = ½ × b × h

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Area  of isosceles triangle formula with three sides .
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Area of isosceles triangle formula with three sides .
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The area of an isosceles triangle is the amount of region enclosed by it in a two-dimensional space. The general formula for the area of triangle is equal to half the product of the base and height of the triangle Here, a detailed explanation about the isosceles triangle area.
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