Find the perimeter of the polygon with vertices

Ответ:

krystalhurst97

15.03.2022

Check the picture below.

so the perimeter of the polygon is the sum of all its sides, namely, AB + BC + CD + DA.

now, let's check how long each side is,

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&A&(~{{ -6}} &,&{{ -4}}~) 
% (c,d)
&B&(~{{ -3}} &,&{{ 6}}~)
\end{array}
\\\\\\
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\
-------------------------------\\\\
AB=\sqrt{[-3-(-6)]^2+[6-(-4)]^2}
\\\\\\
AB=\sqrt{(-3+6)^2+(6+4)^2}
\\\\\\
AB=\sqrt{3^2+10^2}\implies \boxed{AB=\sqrt{109}}\\\\
-------------------------------$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&B&(~{{ -3}} &,&{{6}}~) 
% (c,d)
&C&(~{{ 4}} &,&{{ 0}}~)
\end{array}
\\\\
-------------------------------\\\\
BC=\sqrt{[4-(-3)]^2+[0-6]^2}\implies BC=\sqrt{(4+3)^2+(0-6)^2}
\\\\\\
BC=\sqrt{7^2+(-6)^2}\implies \boxed{BC=\sqrt{85}}\\\\
-------------------------------$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&C&(~{{ 4}} &,&{{0}}~) 
% (c,d)
&D&(~{{ 2}} &,&{{ -1}}~)
\end{array}
\\\\
-------------------------------\\\\
CD=\sqrt{(2-4)^2+(-1-0)^2}\implies CD=\sqrt{(-2)^2+(-1)^2}
\\\\\\
\boxed{CD=\sqrt{5}}\\\\
-------------------------------$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad \\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&D(~{{ 2}} &,&{{-1}}~) 
% (c,d)
&A&(~{{ -6}} &,&{{ -4}}~)
\end{array}\\\\
-------------------------------\\\\
DA=\sqrt{[-6-2]^2+[-4-(-1)]^2}\\\\\\ DA=\sqrt{(-6-2)^2+(-4+1)^2}
\\\\\\
DA=\sqrt{(-8)^2+(-3)^2}\implies \boxed{DA=\sqrt{73}}$

sum those sides up, and that's the perimeter of the polygon.
Find the perimeter of the polygon with vertices a(-6,-4), b(-3,6), c(4,0), and d(2,-1)?

Find the perimeter of the polygon with vertices a(-6,-4), b(-3,6), c(4,0), and d(2,-1)?

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Ответ:

sophiee1021

26.06.2020

Mathematics

b. 72 = amount; is not valid

Step-by-step explanation:

The variable that receives the value(s) must always be on the left side of the equal sign.

It is a convention that makes the sentence more readable and easier to understand. For example, option "a" (total = 9) would be read as: "take variable called 'total' and make its value equal to 9".

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Find the perimeter of the polygon with vertices a(-6,-4), b(-3,6), c(4,0), and d(2,-1)?

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