SOLUTION: I don't know how to do this. Directions: The vertices of an irregular figure are given. Find the area of the figure. T(-4,-2), U(-2,2), V(3,4), W(3,-2)

Question 274213: I don't know how to do this.
Directions: The vertices of an irregular figure are given. Find the area of the figure.
T(-4,-2), U(-2,2), V(3,4), W(3,-2)

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The vertices of an irregular figure are given. Find the area of the figure.
T(-4,-2), U(-2,2), V(3,4), W(3,-2)
--------------------------------------
There's more than one way.
The most obvious is to make it 2 triangles, solve for the lengths and find the areas.
A better way is:
....T. .U. .V. .W ..T
x -4 -2 +3 +3 -4
y -2 +2 +4 -2 -2
-------------------
Multiply the elements with a slope of -1, ie, Tx*Uy, Ux*Vy, etc and add them
Multiply the elements with a slope of +1, ie, Ty*Ux, Uy*Vx, etc and add them
The absolute value of the difference is 2 x the area, divide by 2.
---------------------
(-4*2) + (-2*4) + (3*-2) + (3*-2) = -8 - 8 - 6 - 6 = -28
---------
((-2*-2) + (2*3) + (4*3) + (-2*-4) = 4 + 6 + 12 + 8 = 30
Difference = 58
Area = 29 sq units
------------
This method is good for any number of points. Note that the 1st and last points are the same.

RELATED QUESTIONS
Two verticies of a rectangle are on the x-axis and the other two vertices on the curve... (answered by ikleyn)

Trapezoid RSTU is shown find the length of UT by using the coordinates of vertices U and... (answered by ikleyn)

How do I find the area of a trapezoid? I don't understand so please help (answered by ewatrrr)

How do you find the area of an irregular region? I know that the formula is A=(I+1/2B) x... (answered by jim_thompson5910)

How do u find the area of a composite... (answered by Fombitz)

Perhaps if I could know how to do a problem like this one, I could figure out how to do... (answered by jim_thompson5910)

Find the sum of this series that is not arithmetic or geometric,... (answered by math_tutor2020,ikleyn,greenestamps)

How do you find the area of a diamond figure? The coordinates I have are the following: (answered by Alan3354)

Suppose P and Q' are subsets of U. n(U) = 15, n(P) = 6, and n(Q') = 4. Find a. n(p') b. (answered by ikleyn)