How to Calculate the Sides of an Isosceles Triangle

A right isosceles triangle occurs when the third angle is 90 degrees.

An isosceles triangle is any triangle where two sides have an equal length. The unequal side is named the base. Also, the base angles of an isosceles triangle are equal. To calculate the sides of the isosceles triangle, you must be given the base length and the altitude. The altitude of an isosceles triangle starts at the vertex, or top point of the triangle, and intersects with the base, splitting it in half. This split is called the perpendicular bisector and forms two congruent right angles in the interior of the triangle.

Things You'll Need

• Calculator with square root button

Instructions

1. Learn the correct equation associated with finding the sides of the isosceles triangle, where "S" is the side, "A" is the area and "B" is the base:

   S = square root of A^2 + (B/2)^2

2. Plug your "givens" into the equation. For example, assume you have an equation with givens of 10 for the base and 20 for the area. Rewrite the example equation as:

   S = square root of 20^2 + (10/2)^2

3. Start calculating the example by squaring 20. This equals 400. Then divide 10 by 2 for an answer of 5. Square 5 to yield a result of 25. Rewrite the equation:

   S = square root of 400 + 25

   S = 20.62 when rounded to the nearest hundredth

References

• Oswego City School District Regents Exam Prep Center: Isosceles Triangle Theorems
• Math Open Reference: Isosceles Triangle
• Math Open Reference: Pythagorean Theorem