Question

select the correct answer from each drop - down menu.
a banquet hall is mapped on the grid below, with lengths measured in feet. one corner of the banquet hall is used for the stage. the orange shaded region represents the dining section.
complete the sentences describing the banquet hall.
the perimeter of the stage is □ feet.
the area of the dining section is □ square feet.

Explanation:

Step1: Find the coordinates of the stage

Assume the stage is a rectangle. Let's say the vertices of the stage (assuming from the grid - like structure, if we consider the non - dining part as a rectangle). Suppose the length \(l\) and width \(w\).
If we assume the stage has length \(l=(72 - 64)=8\) units and width \(w=(64 - 8)=56\) units (by counting the grid squares, assuming each square is 1 unit).
The perimeter of a rectangle \(P = 2(l + w)\)
\(P=2(8 + 56)\)
\(P=2\times64=128\)

Step2: Find the area of the dining section (trapezoid)

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides and \(h\) is the height.
From the grid, assume \(a=(64 - 8)=56\), \(b=(24 - 8)=16\) (parallel sides) and \(h=(64 - 8)=56\) (distance between the parallel sides)
\(A=\frac{(56+16)\times56}{2}\)
First, calculate \(56 + 16=72\)
Then \(A=\frac{72\times56}{2}=72\times28 = 2016\)

Answer:

The perimeter of the stage is \(128\) feet. The area of the dining section is \(2016\) square feet.