To find the perimeter of polygon QRSTU, we need to calculate the lengths of each side and then sum them.
The coordinates of the points are:
- Q(2, 0)
- R(4, 5)
- S(8, 7)
- T(6, 4)
- U(10, 3)
We will calculate the lengths of each side using the distance formula, which is:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
-
Length of QR: \[ QR = \sqrt{(4 - 2)^2 + (5 - 0)^2} = \sqrt{(2)^2 + (5)^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.385 \]
-
Length of RS: \[ RS = \sqrt{(8 - 4)^2 + (7 - 5)^2} = \sqrt{(4)^2 + (2)^2} = \sqrt{16 + 4} = \sqrt{20} \approx 4.472 \]
-
Length of ST: \[ ST = \sqrt{(6 - 8)^2 + (4 - 7)^2} = \sqrt{(-2)^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13} \approx 3.606 \]
-
Length of TU: \[ TU = \sqrt{(10 - 6)^2 + (3 - 4)^2} = \sqrt{(4)^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17} \approx 4.123 \]
-
Length of UQ: \[ UQ = \sqrt{(2 - 10)^2 + (0 - 3)^2} = \sqrt{(-8)^2 + (-3)^2} = \sqrt{64 + 9} = \sqrt{73} \approx 8.544 \]
Now, we sum the lengths of all the sides to find the perimeter:
\[ P = QR + RS + ST + TU + UQ \] \[ P \approx 5.385 + 4.472 + 3.606 + 4.123 + 8.544 \approx 26.130 \]
Rounding this to the nearest tenth, we get:
\[ \text{Perimeter} \approx 26.1 \]
Thus, the perimeter of polygon QRSTU is approximately 26.1.