Construct a section of the cube with a plane suitable through the three given points, the points lie in the middle

| June 10, 2021 | education

Construct a section of the cube with a plane suitable through the three given points, the points lie in the middle of its edges extending from one vertex. Find the perimeter of the section if the edge of the cube is equal to a = 10

We will construct points P, M and K – the midpoints of the edges A1D1, C1D1, DD1.

The РMC triangle is our sought-for section.

Let us construct the diagonal A1D of the side face AA1D1D.

In a right-angled triangle АА1D, according to the Pythagorean theorem, we determine the length of the hypotenuse А1D.

A1D2 = AD2 + AA12 = 100 + 100 = 2 * 100.

A1D = 10 * √2 cm.

Since P and K are the middle of the sides, then РK is the middle line of the triangle A1D1D.

РK = A1D / 2 = 5 * √2 cm.

Similarly, РM = MK = РK = 5 * √2 cm.

Then Psech = 3 * РK = 15 * √2 cm.

Answer: The perimeter of the section is 15 * √2 cm.



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