what is the area of the rectangle below?
(-1,4), (-4,-5), (-7,2), (5,2)
20 square root of 13
10 square root of 6
120
60
To find the area of a rectangle, we need to find the length and the width. We can use the distance formula to find the lengths of the sides of the rectangle.
Using the distance formula:
AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
AB = sqrt((-4 - (-1))^2 + (-5 - 4)^2)
AB = sqrt((-3)^2 + (-9)^2)
AB = sqrt(9 + 81)
AB = sqrt(90) = 3sqrt(10)
BC = sqrt((x2 - x1)^2 + (y2 - y1)^2)
BC = sqrt((-7 - (-4))^2 + (2 - (-5))^2)
BC = sqrt((-3)^2 + (7)^2)
BC = sqrt(9 + 49)
BC = sqrt(58)
The length of the rectangle is BC = sqrt(58) and the width of the rectangle is AB = 3sqrt(10).
Now we can calculate the area of the rectangle:
Area = length * width
Area = sqrt(58) * 3sqrt(10)
Area = 3sqrt(58) * sqrt(10)
Area = 3sqrt(580)
Area = 60sqrt(13)
Therefore, the area of the rectangle is 60sqrt(13).