How to find the area of an isosceles triangle
The area of an isosceles triangle depends on the type of isosceles triangle. An Isosceles triangle has at least two sides with the same measurement.
Two special types of isosceles triangles include the isosceles right triangle, in which one of the angles measures 90 degrees, and the equilateral triangle, which has three equal sides. You can calculate each kind of isosceles triangle's area through the measurements of its sides.
Square an equal side's length, then multiply it by four. For this example, an equal side's length is 5, and 5 squared is 25. Four multiplied by 25 equals 100.
Square the third side's length, and then subtract it from the square product in Step 1. For this example, the measurement of the third side is 3, and the square of 3 is 9. Subtracting 9 from 100 results in 91.
- Square an equal side's length, then multiply it by four.
- For this example, the measurement of the third side is 3, and the square of 3 is 9.
Calculate the difference's square root, then divide it by four. For this ongoing example, 9.539 is the square root of 91, and 9.539 divided by 4 equals 2.385.
Multiply the square root product from Step 3 by the third side's measurement for the area of the triangle. For this example, multiplying 3 and 2.385 equals 7.154.
Isosceles right triangle
Obtain the equal sides. With this example, the length of each equal side is 10.
- With this example, the length of each equal side is 10.
Multiply the two lengths of the equal sides together. For this example, 10 multiplied by 10 equals 100.
Divide the equal sides' product in half. For this example, half of 100 is 50.
Square a side's length. For this example, a side has a length of 8, and the square of 8 is 64.
Multiply the side's square by the square root of 3. For this example, 64 multiplied by the square root of 3 equals 110.851.
- For this example, a side has a length of 8, and the square of 8 is 64.
- For this example, 64 multiplied by the square root of 3 equals 110.851.
Find a fourth of the product from Step 2. For this example, dividing 110.851 by 4 equals 27.713.
- The area of any isosceles triangle also is solvable through the equation for general triangular area, which is area = (height * base) / 2, in which base is the length of a selected side and height is the perpendicular measurement from the selected side to an opposite angle.
Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.