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Find the area of rectangle ABCD , with vertices A(1,7) , B(3,7) , C(3,−4) , and D(1,−4)
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Celia is designing a pool for her backyard. It is in the shape of a rectangle, and on her design 1 unit=1 ft. On her graphed design, the corners of the pool are at (28,12) , (18,12) , (18,4) , and (28,4) . What is the area of her pool?
For the first question:
To find the area of rectangle ABCD, we can use the formula for the area of a rectangle which is length x width.
The length of the rectangle can be found using the distance formula:
AB = √[(3-1)^2 + (7-7)^2]
AB = √[(2)^2 + (0)^2]
AB = √[4 + 0]
AB = √4
AB = 2
Similarly, CD = √[(3-1)^2 + (-4-(-4))^2]
CD = √[2^2 + 0^2]
CD = √4
CD = 2
The width of the rectangle can be found using the distance formula between points A and D:
AD = √[(1-1)^2 + (-4-7)^2]
AD = √[0^2 + (-11)^2]
AD = √121
AD = 11
Therefore, the area of rectangle ABCD is:
Area = AB x AD
Area = 2 x 11
Area = 22 square units
For the second question:
Given that the corners of the pool are at (28,12), (18,12), (18,4), and (28,4), the length of the pool is 28-18=10 ft and the width is 12-4=8 ft.
Therefore, the area of Celia's pool is:
Area = length x width
Area = 10 x 8
Area = 80 square feet.