A pentagon is formed by connecting the tips of a starfish's legs, as shown.
6
10
8
11
5
4
What is the area of the pentagon?
A.
143 square centimeters
B.
91.5 square centimeters
C.
44 square centimeters
D.
71.5 square centimeters
To calculate the area of the pentagon, we can divide it into smaller shapes that we can easily calculate the area of. In this case, we can divide the pentagon into a triangle and a trapezoid.
First, let's calculate the area of the triangle. We can see that the base of the triangle is 11 cm and the height is 4.5 cm (half of 9 cm, which is from the top of the pentagon to the base of the triangle).
Area of triangle = (1/2) * base * height
Area of triangle = (1/2) * 11 cm * 4.5 cm
Area of triangle = 24.75 square centimeters
Next, let's calculate the area of the trapezoid. The trapezoid is formed by cutting off one of the corners of the pentagon and creating a smaller triangle on the side, so we need to calculate the area of both the trapezoid and the triangle.
Area of trapezoid = (1/2) * (base1 + base2) * height
Area of trapezoid = (1/2) * (8 cm + 6 cm) * 9 cm
Area of trapezoid = (1/2) * 14 cm * 9 cm
Area of trapezoid = 63 square centimeters
Therefore, the total area of the pentagon is the sum of the area of the triangle and trapezoid.
Total area = 24.75 square centimeters + 63 square centimeters
Total area = 87.75 square centimeters
Thus, the closest option to the calculated area of the pentagon is 91.5 square centimeters, which is option B.