Question
Use the image to answer the question.
A coordinate plane shows a rectangle A B C D plotted in the first quadrant. The x axis and y axis range from negtive 2 to 10. A rectangle A B C D is plotted with points A at left parenthesis 1 comma 1 right parenthesis, B at left parenthesis 1 comma 4 right parenthesis, C at left parenthesis 8 comma 4 right parenthesis, and D at left parenthesis 8 comma 1 right parenthesis. The points are connected by solid lines and the area of the rectangle is shaded.
Hana and Josh want to build a flower box for their grandmother. They measured the space in front of her house and know the perimeter is 20 inches, but they need to calculate the area as well. Using the graph, calculate the area for the flower box.
(1 point)
square inches
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To calculate the area of the rectangle A B C D, we need to find the length of sides AB and BC.
Length of AB:
Using the distance formula:
AB = sqrt[(1-1)^2 + (4-1)^2] = sqrt(0 + 9) = sqrt(9) = 3
Length of BC:
BC = sqrt[(8-1)^2 + (4-4)^2] = sqrt(49 + 0) = sqrt(49) = 7
Therefore, the area of the rectangle is:
Area = AB x BC = 3 x 7 = 21 square inches