Find the area of rectangle QRST, with vertices Q(−1,7), R(5,7), S(5,3), and T(−1,3).

Question

(1 point) units by the power of 2

Answer 1

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.

Answer 2

wrong

Answer 3

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.