SOLUTION: The area of a trapezoidal cornfield IOWA is 18000 sq m. The 100-meter side IO is parallel to the 150-meter side W A. This field is divided into four sections by diagonal roads IW a

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The area of a trapezoidal cornfield IOWA is 18000 sq m. The 100-meter side IO is parallel to the 150-meter side W A. This field is divided into four sections by diagonal roads IW a      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1155229: The area of a trapezoidal cornfield IOWA is 18000 sq m. The 100-meter side IO is parallel to the 150-meter side W A. This field is divided into four sections by diagonal roads IW and OA. Find the areas of the triangular sections.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The area 18000 is the height, multiplied by the average of the two bases:

18000+=+h%28%28100%2B150%29%2F2%29
h+=+18000%2F125+=+144

Let P be the intersection of IW and OA.

Triangles IPO and WPA are similar, with a ratio 100:150 = 2:3.

So the heights of triangles IPO and WPA are 2/5 of 144 and 3/5 of 144.

The area of triangle IPO is %281%2F2%29%28100%29%28%282%2F5%29%28144%29%29+=+2880.

The area of triangle WPA is %281%2F2%29%28150%29%28%283%2F5%29%28144%29%29+=+6480.

The combined area of those two triangles is 9360. So the combined area of the other two triangles is 18000-9360 = 8640.

The areas of those other two triangles are the same (they have the same base and height), so the area of each of them is 4320.

ANSWERS: The areas of the four triangles, in square meters, are
2880
4320
4320
6480