Question

Randall purchased a plot of land for his business. The figure represents a plan of the land showing the location of the office space, parking lot and open space for a yard so that the employees and visitors can enjoy time outside. The coordinates represent points on a rectangular grid with units in feet. How much bigger is the area of the parking lot in comparison to the area of the yard

Answer 1

Answer:

2000 sq. ft.

Step-by-step explanation:

The parking lot is rectangle, so the area is base * height.

Looking at lower coordinates, the base is from x=100 to x = 140, so base is 40.

Looking at first coordinate pair where y = 20 and top coordinate pair where y = 100, so height is 80.

Area of parking lot = 40 * 80 = 3200

Now,

The yard is diamond shape. It can be broken down into 2 triangles. Area of triangle is given by 1/2 * base * height.

First triangle (left one):

Height will be from x = 40 to x = 60, so height is 20.

Base would be 40 to 80, so base is 40.

Area = 1/2 * 40 * 20 = 400

Second triangle (right one):

Height will be from x= 60 to x = 100, height is 40.

Base is same as first triangle, which is 40.

Area = 1/2 * 40 * 40 = 800

Area of Yard = 800 + 400 = 1200

Parking lot is bigger by 3200 - 1200 = 2000 square feet