What is the area of the figure?
what is the area of the figure?

Shoelace formula: you take the x-coordinates of all of the points and write them down, vertically, in order (clockwise or counter) until you write the first number twice. You do the same with the y-coordinates, next to the first list. Then, you multiply the x-coordinate to the y-coordinate that is one down, which makes a shoelace-like formation. Finally, you add all of the numbers on the left and right, find the difference, then divide the absolute value of that by 2.

#1

-1   4

2   2

2  -2

-2 -4

-5 -2

-5  2

-1   5

Left products: 8, 4, 4, 20, 10, -2

Right products: -2, -4, -8, 4, -10, -25

Sums: 44, -45

AV of Difference: 89

Area = 44.5 units²

#2

-1   2

1    5

3   2

3   -1

-5 -3

-5   2

-3   5

Left products: 2, 15, 6, 5, 15, -6

Right products: -5, 2, -3, -9, -10, -25

Sums: 37, -50

AV of difference: 87

Area = 43.5 units²

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

answer: about 22.67

step-by-step explanation: