What is the area of a polygon that has sides that are 12, 3,3,5,5,6,6, and 12
To calculate the area of a polygon with given side lengths, we need to use the formula for the area of a polygon given its side lengths. The formula for finding the area of a polygon with side lengths a, b, c,... is:
Area = sqrt[(s-a)(s-b)(s-c)...]
Where s is the semiperimeter of the polygon, which can be calculated by adding all the side lengths and dividing by 2:
s = (12 + 3 + 3 + 5 + 5 + 6 + 6 + 12) / 2
s = 42 / 2
s = 21
Now we can plug in the side lengths into the formula:
Area = sqrt[(21-12)(21-3)(21-3)(21-5)(21-5)(21-6)(21-6)(21-12)]
Area = sqrt[9 * 18 * 18 * 16 * 16 * 15 * 15 * 9]
Area = sqrt[612706560]
Therefore, the area of the polygon is sqrt(612706560), which is approximately 24751.719 units squared.