Question 1155229
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The area 18000 is the height, multiplied by the average of the two bases:<br>
{{{18000 = h((100+150)/2)}}}
{{{h = 18000/125 = 144}}}<br>
Let P be the intersection of IW and OA.<br>
Triangles IPO and WPA are similar, with a ratio 100:150 = 2:3.<br>
So the heights of triangles IPO and WPA are 2/5 of 144 and 3/5 of 144.<br>
The area of triangle IPO is {{{(1/2)(100)((2/5)(144)) = 2880}}}.<br>
The area of triangle WPA is {{{(1/2)(150)((3/5)(144)) = 6480}}}.<br>
The combined area of those two triangles is 9360.  So the combined area of the other two triangles is 18000-9360 = 8640.<br>
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.<br>
ANSWERS:  The areas of the four triangles, in square meters, are
2880
4320
4320
6480<br>