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: Identify the stage's shape and dimensions

The stage is a rectangle. Let's assume the vertices of the stage rectangle are the non - shaded part in the corner. If we assume the coordinates of the vertices of the stage rectangle are such that the length along the x - axis is \(l_x\) and along the y - axis is \(l_y\). From the grid, if we assume the non - shaded rectangle has length \(l_x=(72 - 64)=8\) feet and width \(l_y=(64 - 56)=8\) feet.
The perimeter of a rectangle is \(P = 2(l + w)\), so \(P=2(8 + 8)=32\) feet.

Step2: Identify the dining section's shape and use area formula

The dining section is a 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.
The parallel sides of the trapezoid: \(a=(64 - 8)=56\) feet, \(b=(64 - 24)=40\) feet, and the height \(h=(72 - 8)=64\) feet.
\[A=\frac{(56 + 40)\times64}{2}=\frac{96\times64}{2}=96\times32 = 3072\] square feet.

Answer:

The perimeter of the stage is 32 feet.
The area of the dining section is 3072 square feet.