Inscribed unit square problem:

Question

A picture has a cross made from five unit squares. The cross is inscribed in a large square whose sides are parallel to the dashed square, formed by four of the vertices of the cross. Find the area of the large outer square?Picture

The picture that you linked to cannot be easily embedded in your question. Can you please link to the actual file, rather than some wonky hosting service? — Xander Henderson, Dec 03 '17 at 04:17

score 1 · Answer 1 · answered Dec 03 '17 at 04:14

1

Hint: how many of those small triangles fit in the border between the big and small square?

answered Dec 03 '17 at 04:14

actinidia

3,365

score 0 · Accepted Answer · answered Dec 03 '17 at 04:16

Each edge of the dashed square has length $\sqrt5$. The difference between that length and one edge of the large square is two altitudes of little right triangles with legs $1$ and $\frac12$. That altitude satisfies the proportion $\frac{x}{1/2}=\frac{1}{\sqrt5/2}$. Therefore, $x=\frac1{\sqrt5}$, and the edge of the large square is $\sqrt5+\frac2{\sqrt5}$.

From there, you should be able to get the area.

score 0 · Answer 3 · answered Dec 03 '17 at 11:01

0

The area of the big square is equal to $5$. I have answered a similar question at here: Area of a square inside a square created by connecting point-opposite midpoint

answered Dec 03 '17 at 11:01

Seyed

8,933

Inscribed unit square problem:

3 Answers3