Question

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.

Answer 1

Answer:

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:

A=\frac{1}{2}(AB+CD)\times ADA=

2

1

(AB+CD)×AD

From the graph, AB = 60 ft, CD = 40 ft, AD = 30 ft

Therefore, the area is given as:

\begin{gathered}A=\frac{1}{2}(60+40)\times 30\\A=\frac{1}{2}\times 100\times 30=1500\ ft^2\end{gathered}

A=

2

1

(60+40)×30

A=

2

1

×100×30=1500 ft

2

Therefore, the area of the floor of the shed is 1500 square feet.