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. a rectangle abcd is plotted on a coordinate plane. rectangle abcd has vertices a at (8, 60), b at (68, 60), c at (68, 8) and d at (8, 8). a line is drawn from a point e (20, 60) to f at (68, 24). the area bounded by afecd in rectangle abcd is shaded. complete the sentences describing the banquet hall. the perimeter of the stage is feet. the area of the dining section is square feet.

Answer 1

The perimeter of the stage is 172 feet. The area of the dining section is 2544 square feet.

Step-by-step explanation:

The perimeter of the stage can be found by summing the lengths of all four sides. In this case, the stage is represented by rectangle ABCD, so the perimeter is the sum of AB + BC + CD + DA. Using the given coordinate points, we can calculate the lengths of the sides: AB = 68 - 8 = 60 feet, BC = 8 - 8 = 0 feet, CD = 8 - 68 = -60 feet, DA = 60 - 8 = 52 feet. Since lengths cannot be negative, we take the absolute value of CD, which is 60 feet. Therefore, the perimeter of the stage is 60 + 0 + 60 + 52 = 172 feet.

The area of the dining section can be found by calculating the area of the shaded region AFEC and subtracting it from the total area of rectangle ABCD. The length of side AE is given as 20 - 8 = 12 feet, and the length of side FC is given as 68 - 20 = 48 feet. Therefore, the area of AFEC is the product of AE and FC, which is 12 * 48 = 576 square feet. The area of rectangle ABCD is the product of the length and width, which is (68 - 8) * (60 - 8) = 60 * 52 = 3120 square feet. Therefore, the area of the dining section is 3120 - 576 = 2544 square feet.