Question

Find the perimeter of the polygon. Round your answer to the nearest tenth.

Answer 1

Answer:

Option B.

Step-by-step explanation:

From the given figure it clear that the the vertices of the polynomial are Q(2,0), R(4,5), S(8,7), T(6,4) and U(10,3).

Distance formula:

$d=\sqrt{(x-2-x_1)^2+(y_2-y_1)^2}$

Using distance formula, we get

$QR=\sqrt{\left(4-2\right)^2+\left(5-0\right)^2}=\sqrt{29}$

$RS=\sqrt{\left(8-4\right)^2+\left(7-5\right)^2}=2\sqrt{5}$

$ST=\sqrt{\left(6-8\right)^2+\left(4-7\right)^2}=\sqrt{13}$

$TU=\sqrt{\left(10-6\right)^2+\left(3-4\right)^2}=\sqrt{17}$

$QU=\sqrt{\left(10-2\right)^2+\left(3-0\right)^2}=\sqrt{73}$

Now, the perimeter of the polynomial is

$Perimeter=QR+RS+ST+TU+QU$

$Perimeter=\sqrt{29}+2\sqrt{5}+\sqrt{13}+\sqrt{17}+\sqrt{73}$

$Perimeter=26.12996$

$Perimeter\approx 26.1$ units.

Therefore, the correct option is B.