1978 AHSME Problems/Problem 29
Problem
Sides ,
,
, and
, respectively of convex quadrilateral
are extended past
,
,
, and
to points
,
,
, and
. If
,
,
, and
, and the area of
is 10, determine the area of quadrilateral
.
Solution
Notice that the area of
is the same as that of
(same base, same height). Thus, the area of
is twice that (same height, twice the base). Similarly, [
] = 2
[
], and so on.
Adding all of these, we see that the area the four triangles around is twice [
] + [
] + [
] + [
], which is itself twice the area of the quadrilateral
. Finally, [
] = [
] + 4
[
] = 5
[
] =
.
~ Mathavi
Note: Anyone with a diagram would be of great help (still new to LaTex).