Question

find the area of the isosceles triangle. the area is square feet.

Explanation:

Step1: Find the height of the triangle

The isosceles triangle is split into two right triangles by the height \( h \). The base of each right triangle is \( \frac{32}{2} = 16 \) ft, and the hypotenuse is 20 ft. Using the Pythagorean theorem \( a^2 + b^2 = c^2 \), where \( c = 20 \) and \( a = 16 \), we solve for \( b = h \):
\[
h = \sqrt{20^2 - 16^2} = \sqrt{400 - 256} = \sqrt{144} = 12
\]

Step2: Calculate the area of the triangle

The formula for the area of a triangle is \( A = \frac{1}{2} \times \text{base} \times \text{height} \). The base is 32 ft and the height is 12 ft:
\[
A = \frac{1}{2} \times 32 \times 12 = 16 \times 12 = 192
\]

Answer:

192