Step 1: Set up formula to calculate a area of the Isosceles triangle.


            1)  Area of an isosceles triangle = \frac{1}{2} b*h

                Where b - base and h - height (altitude)

                                         h (Altitude) = \sqrt{a^2 - \frac{b^2}{4}}

            When Two equal sides – s & s & included angles

          2)  Area of an isosceles triangle = \frac{1}{2}*s^2*\sin\theta

              s is the length of one of the two equal sides.

              θ is the angle between the two equal sides.

Step 2: According to the given data choose the appropriate formula to find the area

      NOTE: In the question the lengths of the triangle are given so use first formula.

Step 3: Calculate the height of the triangle.

            EXAMPLE:    h(Altitude)=\sqrt{a^2-\left(\frac{b}{2}\right)^2}

            height  {\displaystyle h={\sqrt {8^{2}-({\frac {4}{2}})^{2}}}}

                             {\displaystyle ={\sqrt {64-4}}}

                             {\displaystyle ={\sqrt {60}}}

                      Simplify the square root by finding factors:

                        {\displaystyle h={\sqrt {60}}={\sqrt {4*15}}={\sqrt {4}}{\sqrt {15}}=2{\sqrt {15}}.}

Step 4: Plug the base and height into your area formula. 

            EXAMPLE: Area  {\displaystyle ={\frac {1}{2}}bh}

               {\displaystyle ={\frac {1}{2}}(4)(2{\sqrt {15}})}

                {\displaystyle =4{\sqrt {15}}}

          Leave this answer as written, or enter it in a calculator to find a decimal

          estimate (about 15.49 square centimeters).