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Found: 145

Which triangle has the largest area? The dots form a regular grid.

What is the ratio between the red and blue area? All shapes are semicircles.

A circle was inscribed in a square, and another square was inscribed in the circle. Which area is larger, the blue or the orange one?

In his twelfth year on the island Robinson Crusoe managed to tame a wolf, and used him as a guard dog for his goat. He used to tie the wolf with ropes to pegs and other ropes in such a way that there was always a safe place for the goat to escape. Subsequently, he studied the shapes the goat was grazing on the ground.

Draw a picture how Robinson used to tie the goat and the wolf in order for the goat to graze the grass in the shape of a ring

Think of other shapes Robinson’s goat can graze without a wolf, or with a wolf tied nearby. What if Robinson managed to tame several wolves and used them as guard dogs? Can two tied wolves keep an untied goat in a triangle? Can you think of other shapes you can create with Robinson’s goat and wolves?

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 edges of a cube are assigned with integer values. For each vertex we look at the numbers corresponding to the three edges coming from this vertex and add them up. In case we get 8 equal results we call such cube “cute”. Are there any “cute” cubes with the following numbers corresponding to the edges:

(a) \(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\);

(b) \(-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6\)?

The area of a rectangle is 1 cm\(^2\). Can its perimeter be greater than 1 km?