Area of Isosceles Triangle: Formula, Properties & Examples

Area of an isosceles triangle depends upon the available parameters. An isosceles triangle is a type of triangle which has only two sides to be equal. Angles opposite to these two equal sides are also equal. The usual area for the Isosceles triangle is determined by half of the product of base and height of the Isosceles triangle. The area of Isosceles triangle is given by the formula,

A = ½ base x height

Key Takeaways: Isosceles Triangle, Formulas, Base angle theorem, Apex angle

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Isosceles Triangle 

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An isosceles triangle is a type of triangle which has only two equal sides/angles. Angles opposite to these equal sides are also equal.

Isosceles Triangle 

In the above image, ABC is an isosceles triangle where AB & AC sides are equal in length and the opposite angles ∠ABC & ∠ACB are equal.

Also Read: Similarities of Triangle

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Properties of Isosceles Triangle

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Some of the major properties are listed below:

• Two sides are congruent to each other.
• The third side of an isosceles triangle which is unequal to the other two equal sides is called the base of the triangle.
• The two angles opposite to the equal sides are equal to each other and it is called base angles. And this is a theorem called Isosceles triangle base angle theorem.

Isosceles Triangle

• The angle which is not congruent to the other angles (base angles) is called the apex angle.
• Upon drawing an altitude from the apex of an isosceles triangle it divides the triangle into two right-angle triangles.
• The perimeter of an isosceles triangle is the sum of all three sides.

Also Read: Section Formula

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Area of Isosceles triangle

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The area of an isosceles angle is the total region covered by all three sides of the triangle in a 2D space.

To calculate the area we can take help from this figure. 

Let’s take triangle ADC,

Here,

\(AD^2 = a^2 - \frac{b^2}{4}\)

So, Height AD is given by,

\(AD = \sqrt{a^2 - \frac{b^2}{4}}\)

Now, Area of Isosceles triangle = ½ x base x height

\(= \frac{1}{2} \times b \times \sqrt{a^2 - \frac{b^2}{4}}\)

Also Read: Pythagoras Theorem

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Calculation of Area 

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The area of an isosceles triangle can be calculated in various ways depending on the known measures of that isosceles triangle. Let’s look at the other formulae that can be used to calculate the area of an isosceles triangle based on different elements –

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Things to Remember

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• An isosceles triangle has two equal sides/angles.
• Angles opposite to the equal sides are congruent to each other.
• Equal angles are called base angle and the other angle is called apex angle.
• The main formula for calculation the area of an isosceles triangle is - ½ * Base * Height.
• The perimeter of an isosceles triangle is the sum of all the three sides.
• The altitude divides an isosceles triangle into two equivalent right-angled triangles.
• Also, the altitude divides the base into two equal parts.

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