Answer:
192 square feet
Explanation:
You want the area of the isosceles triangle with congruent sides 20 ft and base 32 ft.
Height
The height (h) of the triangle is one leg of a right triangle with hypotenuse 20 ft and the other leg 16 ft. It can be found using the Pythagorean theorem:
h² +16² = 20²
h² = 400 -256 = 144
h = √144 = 12
Area
Then the area of the triangle is ...
A = 1/2bh
A = 1/2(32 ft)(12 ft) = 192 ft²
The area is 192 square feet.
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Additional comment
You recognize the base and hypotenuse of the right triangle have the ratio 16/20 = 4/5. This tells you that the right triangle is a 3-4-5 right triangle with a scale factor of 4. That makes the height 4·3 = 12 feet.
This recognition saves you the effort of using the Pythagorean theorem to find the same number.
Given the side lengths, you can also find the area using Heron's formula:
A = √(s(s -a)(s -b)(s -c)) . . . . . where s=(a+b+c)/2, the semiperimeter
A = √(36(16)(16)(4)) = 6·4·4·2 = 192 . . . . as above