Find the area of the polygon in square units. I don’t know the shape but the lengths 7, 13, 15 and 7.
To find the area of a polygon given the side lengths, we can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:
Area = sqrt(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, given by:
s = (a + b + c) / 2
Given the side lengths of the polygon as 7, 13, 15, and 7, we can calculate the area of the polygon by treating it as two triangles with side lengths 7, 13, and 15, and 7, 7, and 15.
For the first triangle:
s = (7 + 13 + 15) / 2 = 17.5
Area1 = sqrt(17.5(17.5 - 7)(17.5 - 13)(17.5 - 15))
Area1 = sqrt(17.5 * 10.5 * 4.5 * 2.5)
Area1 = sqrt(2043.75)
Area1 ≈ 45.2
For the second triangle:
s = (7 + 7 + 15) / 2 = 14.5
Area2 = sqrt(14.5(14.5 - 7)(14.5 - 7)(14.5 - 15))
Area2 = sqrt(14.5 * 7.5 * 7.5 * 0.5)
Area2 = sqrt(405.9375)
Area2 ≈ 20.1
Therefore, the total area of the polygon is the sum of the areas of the two triangles:
Total Area ≈ Area1 + Area2
Total Area ≈ 45.2 + 20.1
Total Area ≈ 65.3 square units
So, the area of the polygon with side lengths 7, 13, 15, and 7 is approximately 65.3 square units.