How to Calculate the Area of an Isosceles Triangle using the Base and Equal Sides

isosceles Triangle

An isosceles triangle is a triangle that has two sides of equal length

An isosceles triangle is a triangle that has two sides of equal length. This means that two of the angles in the triangle are also equal. The side opposite the equal angles is called the base, while the other two sides are called the legs.

To find the area of an isosceles triangle, you would typically need the base and the height. However, in this case, since we don’t have the height, we can use some properties of an isosceles triangle to find a relationship between the base and the height.

Let’s assume that the two equal sides are of length ‘a’ and the base is of length ‘b’. Also, let’s assume that the height is ‘h’. By drawing an altitude from the top vertex to the base, we can split the isosceles triangle into two congruent right triangles.

Using the Pythagorean theorem, we can find the relationship between ‘a’, ‘b’, and ‘h’. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So, for one of the right triangles:
(a/2)^2 + h^2 = a^2

Simplifying the equation:
a^2/4 + h^2 = a^2
h^2 = a^2 – a^2/4
h^2 = (3a^2)/4

Taking the square root of both sides:
h = √((3a^2)/4)
h = (a√3)/2

Now that we have the height in terms of ‘a’, we can find the area of the isosceles triangle. The area of a triangle is given by the formula: Area = (base * height)/2.

Substituting the values:
Area = (b * (a√3)/2)/2
Area = (ab√3)/4

So, the area of an isosceles triangle is (ab√3)/4, where ‘a’ represents the length of the equal sides and ‘b’ represents the length of the base.

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