# How to find the area of an isosceles triangle?

An isosceles triangle is a triangle with two sides of equal length. The word “isosceles” comes from the Greek word for “equal-sided.” An isosceles triangle also has two angles that are equal to each other. You are here to know the way to find the area of an isosceles triangle? Keep reading to know.

## How to find the area of an isosceles triangle?

Formulas for Finding the Isosceles Triangle Area

A = ½ × b × c × sin(α) is a formula that uses the length of two sides and an angle between them.

Or, A = [c2×sin(β)×sin(α)/ 2×sin(2π−α−β)]

Or, A = ½ × a2

To find the area of an isosceles triangle, multiply the base by the height and divide by 2.

For example, if the base is 8 and the height is 10, the area would be 40.

8 * 10 / 2 = 40

Area of an isosceles triangle

If the base of the isosceles triangle is b and the height is h, then the area is:

A = 1/2 bh

### How do I find the height of an isosceles triangle?

The height of an isosceles triangle can be found by using the Pythagorean theorem a^2 + b^2 = c^2.

For example, if the base of the triangle is 6 cm and the two sides are 8 cm, the height can be found by using the equation:

a^2 + b^2 = c^2.

h^2 = 8^2 – 6^2

Next h = √(8^2 – 6^2)

Next  h = √(64 – 36)

Then h = √28

h = 5.29 cm.

### How do you calculate the height of an isosceles triangle?

If you know the length of the base and the length of one of the sides, you can use the Pythagorean Theorem to calculate the height.

If you know the length of the base and the height, you can use the following formula to calculate the length of the sides:

Length of sides = sqrt(height^2 + (base/2)^2)

### How do you find the height of a triangle given three sides?

If you know the lengths of all three sides of a triangle, you can use Heron’s Formula to calculate the area of the triangle. Once you have the area, you can use that to find the height of the triangle.

Heron’s Formula for the area of a triangle:

A = √(s(s – a)(s – b)(s – c))

Where:

A = the area of the triangle

s = the semiperimeter of the triangle

a, b, and c = the lengths of the sides of the triangle

To find the semi perimeter of the triangle, you need to add together the lengths of the three sides and then divide that number by 2.

Once you have the area of the triangle, you can use that to find the height of the triangle. The height of the triangle is equal to the area of the triangle divided by the length of the triangle’s base.

### What is the base and height of an isosceles triangle?

The base of an isosceles triangle is the length of one of its two equal sides, while the height is the length of the triangle’s line of symmetry or the line that bisects the angle between the two equal sides.

In other words, the base is the length of one side, while the height is the length of the line that goes from the midpoint of the base up to the opposite vertex.