Find the area of square QRST with the following vertices Q(-2, 3), R(1, 0), S(4, 3) and T(1, 6).
make a quick sketch to see how the square is positioned.
so all we need is the length of one side, e.g.. side QR
QR^2 = √(3^2+3^2) = √18
So area = √18 √18 = 18
Find the area of square QRST with the following vertices Q(-2, 3), R(1, 0), S(4, 3) and T(1, 6).
To find the area of a square, we need to know the length of one of its sides.
Let's find the distance between two adjacent vertices Q and R to determine the length of one side of the square.
Using the distance formula:
Distance between two points (x1, y1) and (x2, y2) = sqrt((x2 - x1)^2 + (y2 - y1)^2)
The distance between Q(-2, 3) and R(1, 0) is:
dQR = sqrt((1 - (-2))^2 + (0 - 3)^2) = sqrt((1 + 2)^2 + (-3)^2) = sqrt(3^2 + 9) = sqrt(9 + 9) = sqrt(18)
Now that we have the length of one side of the square, we can find its area.
Since a square's sides are all equal, the area of a square is given by:
Area = side length * side length
So, the area of square QRST is:
Area = (sqrt(18))^2 = 18
Therefore, the area of square QRST is 18 square units.
To find the area of the square QRST, we need to find the length of one of its sides, and then square that length.
To find the length of one side, we can use the distance formula between any two vertices of the square. Let's use the distance formula to find the length QR.
The distance formula is given by:
√((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the length QR:
QR = √((1 - (-2))^2 + (0 - 3)^2)
= √((3)^2 + (-3)^2)
= √(9 + 9)
= √18
= 3√2
Now that we have the length of one side, we can find the area of the square by squaring the length:
Area of square QRST = (side length)^2
= (3√2)^2
= 9 * 2
= 18 square units
Therefore, the area of square QRST is 18 square units.