# Difference between revisions of "1985 AJHSME Problems/Problem 4"

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[[1985 AJHSME Problems]] | [[1985 AJHSME Problems]] | ||

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## Revision as of 20:16, 10 March 2009

## Problem

The area of polygon , in square units, is

## Solution

### Solution 1

Obviously, there are no formulas to find the area of such a messed up shape, but we do recognize some shapes we **do** know how to find the area of.

If we continue segment until it reaches the right side at , we create two rectangles - one on the top and one on the bottom.

We know how to find the area of a rectangle, and we're given the sides! We can easily find that the area of is . For the rectangle on the bottom, we do know the length of one of its sides, but we don't know the other.

Note that , and , so we must have

The area of the bottom rectangle is then

Finally, we just add the areas of the rectangles together to get .

### Solution 2

Let be the area of polygon . Also, let be the intersection of and when both are extended.

Clearly,

Since and , .

To compute the area of , note that

We know that , , , and , so

Thus

Finally, we have

This is answer choice