Question

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

Answer 1

To find the area of rectangle QRST, we will first calculate the length of the base and height of the rectangle.

The base of the rectangle is the distance between points Q and R. Using the distance formula √((x2-x1)^2 + (y2-y1)^2), we have:

Base = √((5-(-1))^2 + (7-7)^2)
= √(6^2 + 0^2)
= √(36)
= 6

The height of the rectangle is the distance between points R and S. Using the distance formula again, we have:

Height = √((5-5)^2 + (7-3)^2)
= √(0^2 + 4^2)
= √(16)
= 4

Now that we have the base and height, we can calculate the area of the rectangle using the formula for the area of a rectangle: Area = base x height.

Area = 6 x 4
Area = 24

Therefore, the area of rectangle QRST is 24 square units.