Problems
Draw how Robinson Crusoe should arrange pegs and ropes so that his goat grazes in the shape of a hexagon. The hexagon doesn’t need to be regular.
Robinson Crusoe’s goat is tied to a single peg with one rope. Draw how Robinson should arrange pegs, ropes, a sliding ring, and a wolf so that the goat grazes in the shape of a half-circle.
Un día, Robinson encontró un lobo en la isla. Se lo llevó consigo y lo ató con una cuerda a una estaca. Robinson observó que la cabra no pastaba en ningún lugar al que pudiera llegar el lobo. ¿Cómo podría Robinson colocar a los dos animales con estacas y cuerdas para que la cabra solo pueda pastar en una región con forma de luna menguante? (ver la figura de abajo)
Draw how Robinson Crusoe should arrange pegs, ropes, and a wolf so that the goat grazes grass in the shape of a half-ring.
On the diagram each number denotes the area of a rectangle it is written into. What are the areas of the other rectangles?
Show how to divide any quadrilateral into \(5\) polygons of equal area.
Line \(AB\) is parallel to line \(CD\) and line \(AD\) is parallel to line \(BE\). Show that triangles \(ADE\) and \(ABC\) have equal areas.
A quadrilateral \(ABCD\) is given. Points \(K\) and \(L\) belong to the side \(AB\) and \(AK=KL=LB\) and points \(N\) and \(M\) belong to the side \(CD\) and \(CM=MN=ND\). Show that the area of the quadrilateral \(KLMN\) is \(\frac13\) of the area of the quadrilateral \(ABCD\).
A quadrilateral \(ABCD\) is given. Point \(M\) is a midpoint of \(AB\) and point \(N\) is a midpoint of \(CD\). Point \(P\) is where segments \(AN\) and \(DM\) meet, point \(Q\) is where segments \(MC\) and \(NB\) meet. Show that the sum of the areas of triangles \(APD\) and \(BCQ\) is equal to the area of the quadrilateral \(MQNP\).
A square was cut with two parallel lines. The perpendicular distance between these two lines is \(6\)cm. One of them goes through the top right corner and the other through the bottom left corner. The three regions obtained this way, two triangles and a parallelogram, have equal areas. What is the area of the square?
