Are you smarter than an old book?

Geometry Level 3

In the figure above there are 4 rectangles, 4 right triangles, and a square hole.

a) Determine the sum of the 8 areas (do not include the area of the hole).

b) Let x be the length of DE, and y the height from point A to DE. Calculate $\frac { xy }{ 2 }$ .

Can you explain why parts (a) and (b) have the same result?

The problem has a writing issue You may rearrange the inner pieces so the hole is no longer there Because calculating individual areas is the same as calculating the complete area The hole does not affect the result The figure ADE is not a triangle