Area of black Square?

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- Oct 21st 2013, 08:03 AMparmisarea
Area of black Square?

- Oct 21st 2013, 09:01 AMphys251Re: area
We need more information before we can help you. Surely the problem gives you more detail than this.

- Oct 21st 2013, 06:15 PMSorobanRe: area
Hello, parmis!

I will assume that the side of the square is trisected.

Quote:

Area of black square?

Code:`A x E x F x B`

* - - - * - - - * - - - *

| * * * * * |

| * .*. * |

| * .*:::*. * J |

3x | *:::::::* | 3x

| * *:::* * |

| * * * |

| *θ *θ * * |

* - - - * - - - * - - - *

D x G x H x C

Let the side of square be

Let

Note the right triangle at the upper-right.

Code:`x`

F * * * * * * * B

* θ *

* *

* *

*

J

Hence: .

This is the side of the shaded square.

Area of shaded square: .

In right triangle

Hence: .

Substitute into [1]: .

The area of square

Therefore: .

The area of the shaded square is one-thirteenth that of the original square.

- Oct 23rd 2013, 06:22 AMbjhopperRe: area
I agree with second poster.

Using Sorobans diagram where the slopes of diagonals are3/2,Iget a rhombus in the middle area = 1/12 of square - Oct 24th 2013, 04:05 PMjohngRe: area
Hi all,

I agree with the first response. More information should have been given. Also bjhopper is correct in asserting that the inner quadrilateral is a non-square rhombus when the outer quadrilateral is square. The attachment shows what I think is a reasonable interpretation of the problem and a solution for the area of the inner square.

Attachment 29570