Carey F.

# prove that a square ABCD is half the area of a square ACEF, when the segment AB is half of the segment AE

F

A______B______E

C______D

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Daniel O.

You could also prove it using pythagoras theorem and the fact that the area of a square is equal to the side length squared.

Area of ABCD = AB^2

You could also write the area of ABCD as (using AB = 0.5*AE thus AE = 2*AB): (0.5*AE)^2 = (0.5*2*AB)^2 = AB^2

Area of ACEF = AC^2

Use pythag to find length of AC: AC^2 = AB^2+BC^2 = AB^2+AB^2 = 2*AB^2

Note that the area of ACEF = AC^2 = 2*AB^2 = 2*(area of ABCD) so the area of ABCD is half that of ACEF.

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11/02/12

Patricia C.

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08/26/15

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