Find the area of the polygon in square units. 7 , 13 , 15 , and 7.
To find the area of the polygon with side lengths of 7, 13, 15, and 7, we first need to find the semi-perimeter (s) of the polygon using the formula:
s = (a + b + c + d) / 2
s = (7 + 13 + 15 + 7) / 2
s = 42 / 2
s = 21
Next, we can use Heron's formula to calculate the area of the polygon:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
Area = sqrt(21 * (21 - 7) * (21 - 13) * (21 - 15))
Area = sqrt(21 * 14 * 8 * 6)
Area = sqrt(21 * 672)
Area = sqrt(14112)
Area ≈ 118.75
Therefore, the area of the polygon is approximately 118.75 square units.