SOLUTION: P is any point inside a rectangle. Lines are drawn from P to the four vertices of the rectangle. If the areas are named A1, A2, A3, and A4, prove that A1+A3 equals half the rectang

Question 1117399: P is any point inside a rectangle. Lines are drawn from P to the four vertices of the rectangle. If the areas are named A1, A2, A3, and A4, prove that A1+A3 equals half the rectangle.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The bases of triangles A1 and A3 are two of the parallel sides of the rectangle; call it the length.

The two altitudes of triangles A1 and A3 together are then the width of the rectangle.

Then the sum of the areas of A1 and A3, using the standard formula for the area of a triangle, is one-half the length of the rectangle times the width of the rectangle.

But the area of the rectangle is length times width; therefore the sum of the areas of A1 and A3 is half the area of the rectangle.
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