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.
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
1 answer
1 answer