SOLUTION: Quadrilateral ABCD has a perimeter of 64 cm with measurements as shown. What is the area of the quadrilateral? diagram: http://imgur.com/a/W0NlZ I'm not sure how to do this q

Algebra ->  Surface-area -> SOLUTION: Quadrilateral ABCD has a perimeter of 64 cm with measurements as shown. What is the area of the quadrilateral? diagram: http://imgur.com/a/W0NlZ I'm not sure how to do this q      Log On


   

Question 1055099: Quadrilateral ABCD has a perimeter of 64 cm with measurements as shown. What is the area of the quadrilateral?
diagram: http://imgur.com/a/W0NlZ
I'm not sure how to do this question, could you please help? Thanks in advanced.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Labeling segment AC as d,
segment AD as c,
segment DC as a,

First you can find if you like, d, as part of the upper right triangle.
d%5E2=6%5E2%2B8%5E2
d=sqrt%2836%2B64%29
d=sqrt%28100%29
d=10


Now deal with perimeter for the entire figure and Pythagorean relationship of the lower Triangle ACD.
system%286%2B8%2Ba%2Bc=64%2C100%2Ba%5E2=c%5E2%29
Notice that this uses two unknown variables a and c in two equations, so solvable.