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Question

A coordinate plane shows a rectangle A B C D plotted in the first quadrant with side A D on the x axis. The x axis and y axis range from negative 2 to 10. A rectangle A B C D is plotted with points A at left parenthesis 1 comma 0 right parenthesis, B at left parenthesis 1 comma 5 right parenthesis, C at left parenthesis 7 comma 5 right parenthesis, and D at left parenthesis 7 comma 0 right parenthesis. The points are connected by solid lines and the area of the rectangle is shaded.

A marching band is holding a fundraiser to get new carpeting in the band room. They need to calculate the area of the room so that they can purchase enough carpeting. What is the area of the band room?

(1 point)
Responses

30 ft.2
30 ft. squared

11 ft.
11 ft.

60 ft.2
60 ft. squared

22 ft.

Answer 1

To find the area of rectangle A B C D, we first need to determine the length of its sides.

The coordinates of the rectangle are:

• A (1, 0)
• B (1, 5)
• C (7, 5)
• D (7, 0)

Length of side AB (vertical side):

• The y-coordinates of points A and B are 0 and 5, respectively.
• Length of AB = 5 - 0 = 5 units.

Length of side AD (horizontal side):

• The x-coordinates of points A and D are 1 and 7, respectively.
• Length of AD = 7 - 1 = 6 units.

Now, using the formula for the area of a rectangle (Area = length × width), we calculate:

Area = Length of AB × Length of AD
Area = 5 × 6 = 30 square units.

Thus, the area of the band room is 30 ft².

The correct response is: 30 ft.² or 30 ft squared.