Find the area of rectangle QRST, with vertices Q(−1,7), R(5,7), S(5,3), and T(−1,3).
(1 point) units by the power of 2
To find the area of the rectangle QRST, we can use the formula for the area of a rectangle which is length x width.
Length = QR = distance between points Q and R
Width = QS = distance between points Q and S
Using the distance formula √[(x2 - x1)^2 + (y2 - y1)^2]:
Length QR = √[(5 - (-1))^2 + (7 - 7)^2] = √[6^2 + 0^2] = √36 = 6 units
Width QS = √[(5 - (-1))^2 + (3 - 7)^2] = √[6^2 + (-4)^2] = √[36 + 16] = √52 = 2√13 units
Therefore, the area of rectangle QRST is:
Area = Length x Width = 6 units x 2√13 units = 12√13 square units.
wrong
To find the area of a rectangle, we can use the formula:
Area = length x width
First, we need to find the length and width of the rectangle QRST.
The length of the rectangle QRST can be found by the distance formula:
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length QR = √[(5 - (-1))^2 + (7 - 7)^2]
Length QR = √[6^2 + 0^2]
Length QR = √36
Length QR = 6 units
The width of the rectangle QRST can be found by the distance formula:
Width = √[(x2 - x1)^2 + (y2 - y1)^2]
Width QS = √[(5 - (-1))^2 + (3 - 7)^2]
Width QS = √[6^2 + (-4)^2]
Width QS = √[36 + 16]
Width QS = √52
Width QS = 2√13 units
Now, we can find the area of the rectangle QRST:
Area = Length x Width
Area = 6 units x 2√13 units
Area = 12√13 square units
Therefore, the area of rectangle QRST is 12√13 square units.