SOLUTION: Find the area of the figure. Round to the nearest tenth if necessary. T(-1,8), U(3,5), V(4,0), R(-3,0), S(-3,5)

Algebra ->  Length-and-distance -> SOLUTION: Find the area of the figure. Round to the nearest tenth if necessary. T(-1,8), U(3,5), V(4,0), R(-3,0), S(-3,5)      Log On


   

Question 1113940: Find the area of the figure. Round to the nearest tenth if necessary.
T(-1,8), U(3,5), V(4,0), R(-3,0), S(-3,5)
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
Use Shoelace Theorem.

-1.....8
3.....5
4.....0
-3.....0
-3.....5
-1.....8

A = 1/2 * |-44 - 39| = 41.5

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

If you make a sketch, you will see that the entire figure is the union

of the trapezoid  RSUV  and the triangle STU.



Trapezoid RSUV  has the bases  RV = 7 units;  SU = 6 units  and the height of 5 units.

Its area is  %28%286%2B7%29%2F2%29%2A5 = 65%2F2  square units.



Triangle STU has the base SU = 6 units long and the height of 3 units;

its area is, therefore,  %281%2F2%29%2A6%2A3 = 18%2F2  square units.



The total area is the sum  65%2F2 + 18%2F2 = 83%2F2 = 41 1%2F2 square units.

Solved elementary, at the level accessible to an average 7-th - 8-th grade student.