+0

# Pls help

0
109
5

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

Feb 25, 2020
#3
+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
+1

Hi Heureka,

I am just saying this so you will understand what the problem is next time.  Melody  Feb 25, 2020
edited by Melody  Feb 25, 2020
#5
+2

Hi Melody,

many thanks for the detailed answer! heureka  Feb 25, 2020