Question

Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon.

TYSM

Answer 1

Area of the polygon = 59 in²

Step-by-step explanation:

From the given diagram, we can note that the given polygon is composed of an upper triangle, a side triangle and a rectangle

Therefore:

Area of polygon =

area of upper triangle + area of side triangle + area of rectangle

1- getting the area of the upper triangle:

We have:

base of triangle = 7 in

height of triangle = 6 in

Therefore:

Area of upper triangle =
`(1)/(2)*base*height = (1)/(2)*7*6=21` in²

2- getting the area of the side triangle:

We have:

base of triangle = 4 in

height of triangle = 5 in

Therefore:

Area of upper triangle =
`(1)/(2)*base*height = (1)/(2)*4*5=10` in²

3- getting the area of the rectangle:

We have:

length of rectangle = 7 in

width of rectangle = 4 in

Therefore:

Area of rectangle = length x width = 7 x 4 = 28 in²

4- getting the total area of the polygon:

Area of polygon =

area of upper triangle + area of side triangle + area of rectangle

Therefore:

Area of polygon = 21 + 10 + 28 = 59 in²

Hope this helps :)