Krishna
0

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

FORMULAS:

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