MATH SOLVE

4 months ago

Q:
# A home plate marker for a softball field is a pentagon with three right angles and two congruent angles, as shown in the diagram. The ground crew for a softball complex has 4 home plate markers to paint. Calculate the area of the 4 home plate markers. The measurements shown in the diagram are in inches. A. 50 in.² B. 162 in.² C. 648 in.² D. 848 in.²

Accepted Solution

A:

The figure needed to answer the question is attached.

You can split the pentagon in two figures: a) a rectangle with side lentghs equal to 14 inches and 8 inches, and b) a right isosceles triangle with base 10 inches and height 10 inches.

a) area of the rectangle: base * height = 14in * 8 in = 112 in^2

b) area of the triangle: (1/2) base * height = (1/2) 10 in * 10 in = 50 in^2

Area of the pentagon = 112 in^2 + 50 in^2 = 162 in^2

Area of 4 pentagons = 4 * 162 in^2 = 648 in^2.

Answer: option C. 648 in^2

You can split the pentagon in two figures: a) a rectangle with side lentghs equal to 14 inches and 8 inches, and b) a right isosceles triangle with base 10 inches and height 10 inches.

a) area of the rectangle: base * height = 14in * 8 in = 112 in^2

b) area of the triangle: (1/2) base * height = (1/2) 10 in * 10 in = 50 in^2

Area of the pentagon = 112 in^2 + 50 in^2 = 162 in^2

Area of 4 pentagons = 4 * 162 in^2 = 648 in^2.

Answer: option C. 648 in^2