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

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)