What is the area of the polygon? Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles
12 3 4 4 2
To find the area of the polygon, we need to first find the perimeter of the polygon. The perimeter is the sum of all the side lengths.
Perimeter = 12 + 3 + 4 + 4 + 2 = 25
Next, we can use Heron's formula to calculate the area of the polygon. Heron's formula states that the area of a triangle with sides of length a, b, and c is given by:
Area = √[s(s-a)(s-b)(s-c)]
Where s is the semiperimeter of the triangle (s = (a + b + c) / 2).
In this case, the sides of the polygon are 12, 3, 4, 4, and 2. We can split the polygon into a triangle with sides 3, 4, and 4, and a trapezoid with bases 12 and 2.
Triangle:
s = (3 + 4 + 4) / 2 = 5.5
Area_triangle = √[5.5(5.5-3)(5.5-4)(5.5-4)] = √[5.5(2.5)(1.5)(1.5)] = √(82.875) ≈ 9.11
Trapezoid:
Height of the trapezoid = 4
Area_trapezoid = (1/2)(12 + 2)(4) = 28
Total area of the polygon = Area_triangle + Area_trapezoid = 9.11 + 28 = 37.11
Therefore, the area of the polygon is approximately 37.11 square units.