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# Pls help

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The vertices of a convex pentagon are (-1,-1), (-3,4), (1,7), (6,5), and (3,-1). What is the area of the pentagon

Feb 25, 2020

#1
+1

you can use shoelace

from there you would get

-1 -1

-3  4

1   7

6   5

3  -1

1  -1

so the answer is 47

Feb 25, 2020
#3
+24388
+2

The vertices of a convex pentagon are (-1,-1), (-3,4), (1,7), (6,5), and (3,-1).
What is the area of the pentagon .

Use the Gauss's shoelace area formula. Fill the table in counterclockwise.

$$\begin{array}{|lll|} \hline \mathbf{\text{The area of a convex pentagon } }: \\ \begin{array}{r|rr|c} \hline \text{Point} & x & y & \text{cross products} \\ \hline (-1,~-1): & -1 & -1 \\ & & & (-1)*(-1) -(3)*(-1) \\ (3,~-1): & 3 & -1 \\ & & & 3*5 -6*(-1) \\ (6,~5): & 6 & 5 & \\ & & & 6*7-1*5 \\ (1,~7): & 1 & 7 & \\ & & & 1*4 -(-3)*7 \\ (-3,~4): & -3 & 4 & \\ & & & (-3)*(-1) -(-1)*4 \\ (-1,~-1): & -1 & -1 & \\ \hline & & & \text{sum }~=1+3+15+6+42-5+4+21+3+4 \\ & & & \mathbf{=94} \\ \hline \end{array}\\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline \text{The area of the convex pentagon} &=& \dfrac{1}{2}*\text{sum} \\\\ &=& \dfrac{94}{2} \\\\ &=& \mathbf{47} \\ \hline \end{array}$$

Source "Gauss's magic shoelace area formula and its calculus companion" see:

Feb 25, 2020
#4
+108679
+1

Hi Heureka,

I am just saying this so you will understand what the problem is next time.

Thanks to guest too although your answer is cryptic.

Melody  Feb 25, 2020
edited by Melody  Feb 25, 2020
#5
+24388
+2

Hi Melody,

many thanks for the detailed answer!

heureka  Feb 25, 2020