A rectangle is made up from six squares. Find side length of the largest square if side length of the smallest square is 1.
This shape below is made up from squares.
Find side length of the bottom square if side length of the smallest square is equal to 1.
You are given a convex quadrilateral. Is it always possible to cut out a parallelogram out of the quadrilateral such that three vertices of the new parallelogram are the vertices of the old quadrilateral?
The area of a rectangle is 1 cm\(^2\). Can its perimeter be greater than 1 km?
Which rectangles with whole sides are there more of: with perimeter of 1996 or with perimeter of 1998? (The rectangles \(a \times b\) and \(b \times a\) are assumed to be the same).
A quadrilateral is given; \(A\), \(B\), \(C\), \(D\) are the successive midpoints of its sides, \(P\) and \(Q\) are the midpoints of its diagonals. Prove that the triangle \(BCP\) is equal to the triangle \(ADQ\).
Does there exist a flat quadrilateral in which the tangents of all interior angles are equal?