1985 AJHSME Problems/Problem 4
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
See Also
1985 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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