In a grid of a backyard, the vertices of the floor of a shed are (20, 80), (50, 60), (50, 20), and (20, 20). The coordinates are measured in feet. Find the area of the floor of the shed.
Accepted Solution
A:
Answer:The area of the floor of the shed is 1500 square feet.Step-by-step explanation:Given:The vertices of the floor of a shed are: (20,80), (50,60), (50,20) and (20,20)Let us plot the given vertices on a graph.From the graph, it is clear that the given figure is a trapezium with opposite parallel sides being parallel to the y axis. The height of the trapezium is the side that is parallel to x axis.The area of the trapezium ABCD is given as:[tex]A=\frac{1}{2}(AB+CD)\times AD[/tex]From the graph, AB = 60 ft, CD = 40 ft, AD = 30 ftTherefore, the area is given as:[tex]A=\frac{1}{2}(60+40)\times 30\\A=\frac{1}{2}\times 100\times 30=1500\ ft^2[/tex]Therefore, the area of the floor of the shed is 1500 square feet.