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Question
Find the area of the polygon.
20ft. ,5ft, and 12 ft.
Responses
A 125
125 ft 2
B 140
140 ft 2
C 165
165 ft 2
D 345
345 ft 2
E 375
375 ft 2
To find the area of a polygon with sides of length 20 ft, 5 ft, and 12 ft, we can use Heron's formula.
First, we need to calculate the semi-perimeter (s) of the triangle. This can be done by adding up the lengths of all the sides and dividing by 2:
s = (20 + 5 + 12) / 2
s = 37 / 2
s = 18.5
Next, we can calculate the area using Heron's formula:
Area = sqrt(s * (s - side1) * (s - side2) * (s - side3))
Area = sqrt(18.5 * (18.5 - 20) * (18.5 - 5) * (18.5 - 12))
Area = sqrt(18.5 * (-1.5) * 13.5 * 6.5)
Area = sqrt(2019.375)
Area = 44.94 (rounded to 2 decimal places)
Therefore, the area of the polygon is approximately 44.94 ft^2.
None of the given options match this answer, so it is possible that there may be an error in the provided answer choices.