Getting 3 rectangles
Let’s start by getting 3 rectangles.
Then fold the sheet in half again.
Make one cut along the applied mowing line.
Expand the sheets and get 3 rectangles.
Got 3 rectangles
There are doubts?
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Mathematics is the science of structures, order and relationships, historically developed on the basis of the operations of counting, measuring and describing the shape of objects.
On a sheet of paper folded 2 times, make one straight cut to get:
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Getting 4 triangles and 1 octagon
Let’s look at the steps how to get 4 triangles and 1 octagon.
Apply the cut line to the resulting square.
Make one cut along the applied mowing line of the cut.
Expand the sheets and get 1 octagon and 4 triangles.
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4 triangles and 1 octagon
Cut the rectangle in two cuts into two triangles
Rectangle ABCD was cut into 2 triangles and a quadrilateral. These parts are shown on the right. Swipe in rectangle ABCD of the cut line cut.
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Let’s make the task easier to understand
First of all, you need to understand that we are talking about nothing else than a geometric figure. A rectangular cake is nothing like a rectangle! To solve the problem, you need to get the following shapes:
A quadrilateral is a figure with 4 vertices, it can be a square, a rectangle (as subspecies of a quadrilateral), or a trapezoid or an arbitrary shape with the required number of corners.
Triangles can also be different, acute-angled, obtuse-angled, rectangular and others. Since in the problem statement we are talking about a rectangle, it is worth thinking about the cut option in such a way as to get a right-angled triangle.
Getting 1 hexagon and 2 triangles
Roll the sheet in half again.
Apply the cut line to the resulting square.
Let’s make one cut along the previously applied mowing line.
Expand parts of our sheet and get 1 hexagon and 2 triangles.
Cut correctly into pieces
How a given rectangle should be cut into two parts so that they can be folded: 1) a triangle, 2) a parallelogram (other than a rectangle), 3) a trapezoid?
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How can an equilateral triangle be cut into: 1) two equal triangles; 2) three equal triangles; 3) four equal triangles; 4) six equal triangles; 5) eight; 6) twelve?
Two equal squares are given. How to cut each of them into two parts so that the resulting parts can be folded into a square?
How to divide a given rectangle by two rectilinear cuts into two equal pentagons and two equal right-angled triangles?
Two unequal squares are given. How should they be cut into such pieces so that a third square can be folded out of them? How is the side length of the third square expressed in terms of the side lengths of two data?
A rectangular chocolate bar consists of mn single square slices. How many breaks do you need to make (one piece breaks at a time) to break this tile into single square pieces?
How many cuts must be made with planes so that from a cube with an edge of 3 dm we get cubes with an edge of 1 dm?
A right-angled triangle is given. How should you cut it into two such parts so that from them (without turning the back side) you can fold a triangle symmetrical to this one with respect to one of its legs?
Given triangle ABC. How to cut it into pieces so that from them (without turning the back side) it is possible to fold a triangle symmetrical to the given one with respect to the base of the speaker?
Cut the square into pieces, as shown in Figure 49, mix them and then fold: 1) the same square; 2) a right-angled isosceles triangle; 3) a rectangle other than a square; 4) a parallelogram other than a rectangle; 5) trapezoid.
A painted cube with an edge of 10 cm was sawn into cubes with a rhombus of 1 cm. How many cubes will be obtained: 1) with one painted edge; 2) with two; 3) with three; 4) have no painted edges at all?
How to cut a rectangle with sides 16 and 9 cm into two parts so that a square can be folded out of them? (The cut may be in the form of a broken mowing line.)
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Copy each of the shapes in Figure 50 and cut it into 4 equal pieces.
1) How to cut a given right-angled triangle into acute-angled triangles? 2) How to cut a given arbitrary triangle into acute-angled triangles?
Inside the convex column, 10 points are marked, of which no three lie on one straight line. The polygon is cut into triangles so that all the vertices of the given stoagon and all the given ten points serve as their vertices. How many triangles will there be?