Find the area of rectangle QRST , with vertices Q(−1,7) , R(5,7) , S(5,3) , and T(−1,3) .
To find the area of the rectangle QRST, we can use the formula for the area of a rectangle, which is given by:
Area = length x width
First, we need to find the length and width of the rectangle QRST. To do this, we can calculate the distance between the points Q and R, which will give us the length, and the distance between Q and T, which will give us the width.
Length:
Distance between Q (-1,7) and R (5,7) = √[(5-(-1))^2 + (7-7)^2]
= √[6^2 + 0^2]
= √36
= 6
Width:
Distance between Q (-1,7) and T (-1,3) = √[(-1-(-1))^2 + (7-3)^2]
= √[0^2 + 4^2]
= √16
= 4
Therefore, the length of the rectangle QRST is 6 units and the width is 4 units.
Now, we can calculate the area of the rectangle by multiplying the length and width:
Area = length x width
Area = 6 x 4
Area = 24
So, the area of the rectangle QRST is 24 square units.