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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 x y 2 \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

Franderly Acosta Valdez by Franderly Acosta Valdez , 24, Dominican Repu…

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1 solution

Michael Mendrin
Dec 10, 2015

Ratio 3:5 is not same as 5:8. Close but no cigar.

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Interesting that those are fibonacci numbers 3,5,8 that struct similiar further 13:8,21:13... that converge to Triangle with two angles arctg ((√5+1)/2)

Nikola Djuric - 5 years, 6 months ago

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