Question

Find the perimeter of the figure with the given vertices. QPYXWVUTSR and round to the nearest tenth

Answer 1

To find the perimeter we need to find the lenght of each segment.

The vertexes of the figure are P(-3,0), Q(-5,3), R(0,3), S(3,5), T(5,2), U(2,0), V(5,-2), W(3,-5), X(0,-3) and Y(-5,-3).

We are going to use the formula:

`d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Now, to simpligy things we notice from the figure (and it is confirmed by the points) that it is symmetric across the x-axis, so we won't need to find all the distances; we are only going to find d(P,Q), d(Q,R), d(R,S), d(S,T), d(T,U), so let's do that:

`\begin{gathered} d(P,Q)=\sqrt[]{(-5-(-3))^2+(3-0)^2} \\ =\sqrt[]{13} \end{gathered}`
`\begin{gathered} d(Q,R)=\sqrt[]{(0-(-5))^2+(3-3)^2} \\ =5 \end{gathered}`
`\begin{gathered} d(R,S)=\sqrt[]{(3-0)^2+(5-3)^2} \\ =\sqrt[]{13} \end{gathered}`
`\begin{gathered} d(S,T)=\sqrt[]{(5-3)^2+(2-5)^2} \\ =\sqrt[]{13} \end{gathered}`
`\begin{gathered} d(T,U)=\sqrt[]{(2-5)^2+(0-2)^2} \\ =\sqrt[]{13} \end{gathered}`

With this lengths we can find half of the perimeter, we add them to get:

`5+4\sqrt[]{13}`

Hence, the perimeter is:

`\begin{gathered} P=10+8\sqrt[]{13} \\ =38.8 \end{gathered}`