Question

a contractor is installing baseboards in an irregularly shaped conference room. he consults the blueprints for the room, shown on the graph. how many linear feet of baseboards will he need to finish the room? enter the unknown segment length(s), then calculate the perimeter of the polygon. perimeter of the pentagon: feet

Explanation:

Step1: Calculate length of ZO

Use distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $Z(-3,2)$ and $O(16,20)$, $x_1=-3,y_1 = 2,x_2=16,y_2 = 20$.
$ZO=\sqrt{(16+3)^2+(20 - 2)^2}=\sqrt{19^2+18^2}=\sqrt{361+324}=\sqrt{685}\approx 26.17$

Step2: Calculate length of OQ

For $O(16,20)$ and $Q(21,2)$, using distance formula:
$OQ=\sqrt{(21 - 16)^2+(2 - 20)^2}=\sqrt{5^2+(-18)^2}=\sqrt{25 + 324}=\sqrt{349}\approx18.68$

Step3: Calculate length of QZ

For $Q(21,2)$ and $Z(-3,2)$, since $y$-coordinates are the same, length $QZ=21-(-3)=24$

Step4: Calculate perimeter

Perimeter $P=18 + 19+26.17+18.68+24$
$P = 105.85$

Answer:

$105.85$