Isosceles Triangle

An isosceles triangle is a triangle that has two sides of equal length. These two equal sides are called the legs, and the third side is called the base. The angles opposite the equal sides are also equal.

Properties of Isosceles Triangle

• Two sides are of equal length
• Two angles are of equal measure
• The angle opposite the base is called the vertex angle
• The base angles (angles that have the base as one of their sides) are equal to each other

Formulas for Isosceles Triangle

In an isosceles triangle with base b and legs a, the following formulas apply:

Perimeter = 2a + b

Area = (b/4) * √(4a^2 - b^2)

Example Problem

Find the perimeter and area of an isosceles triangle with base length of 6 cm and each leg length of 5 cm.

Perimeter = 2 * 5 cm + 6 cm = 10 cm + 6 cm = 16 cm

Area = (6/4) * √(4*5^2 - 6^2) = (6/4) * √(100 - 36) = (6/4) * √64 = 6 * 8 = 48 cm²

Practice Problems

1. Find the perimeter and area of an isosceles triangle with base length of 8 cm and each leg length of 10 cm.
2. If the vertex angle of an isosceles triangle measures 60 degrees, what are the measures of the base angles?
3. Find the area of an isosceles triangle with base length of 12 cm and each leg length of 9 cm.