Find the area of the polygon. The lengths are 5,5,6,3,3 and 12, 12.
To find the area of the polygon, we need to first divide it into triangles and then calculate the area of each triangle separately.
The polygon can be divided into two triangles:
Triangle 1: Sides of length 5, 5, and 6 (use 6 as the base)
Triangle 2: Sides of length 3, 3, and 12 (use 12 as the base)
First, let's calculate the area of Triangle 1:
Using Heron's formula,
s = (a + b + c) / 2 = (5 + 5 + 6) / 2 = 8
Area = √[s(s - a)(s - b)(s - c)]
Area = √[8(8 - 5)(8 - 5)(8 - 6)]
Area = √[8(3)(3)(2)]
Area = √[144]
Area ≈ 12
Next, let's calculate the area of Triangle 2:
s = (a + b + c) / 2 = (3 + 3 + 12) / 2 = 9
Area = √[9(9 - 3)(9 - 3)(9 - 12)]
Area = √[9(6)(6)(-3)]
Area = √[324]
Area ≈ 18
Therefore, the total area of the polygon is the sum of the areas of Triangle 1 and Triangle 2:
Total Area ≈ 12 + 18 = 30
So, the area of the polygon is approximately 30.