For a cube with shuttle length of 2, in ABCD A1 B1 C1 D1, M is the middle point of edge Aa1, and the area of the cross section is 0 The answer is 9 / 2 I don't know. The answer in the book is 9 / 2

For a cube with shuttle length of 2, in ABCD A1 B1 C1 D1, M is the middle point of edge Aa1, and the area of the cross section is 0 The answer is 9 / 2 I don't know. The answer in the book is 9 / 2

I changed it and drew a picture below
Extending d1m to Da, intersecting e, connecting CE to AB, intersecting F, the cross section is mfcd1
If the similarity ratio is 2, the area ratio is 4, and the area of triangle EFM is 1 / 3 of mfcd1
The data of triangle EFM is given in the figure, which is a good calculation
Cosine theorem: MF ^ 2 = EF ^ 2 + FM ^ 2-2 * EF * fmcosa (a is the angle between EF and FM)
Cosa = 4 / 5
So Sina = 3 / 5
So the area of EFM is s = 1 / 2 * EF * FM * Sina = 3 / 2
So cross section area = 3S = 9 / 2

In the cube abcd-a1b1c1d1 with edge length 2, M is the midpoint of edge Aa1. What is the cross-section area of cube through C M D1?

Take the midpoint n of AB, because Mn is parallel to A1B, so Mn is parallel to CD1, so the cross section is trapezoidal mncd1
The trapezoidal upper sole Mn = √ 2, the lower sole CD1 = 2 √ 2, the two waist MD1 = CN = √ 5,
From this, we can find that the height of the trapezoid is equal to 3 / √ 2, so the area is equal to 9 / 2

Cube abcd-a1b1c1d1, edge length is a, find the distance from point D1 to section c1bd
Cube abcd-a1b1c1d1, edge length is a, find the distance from point D1 to section c1bd
Calculation by equal product method

The volume of b-c1d1d is 1 / 3 * a * 1 / 2 * A & sup2;
The volume of d1-c1bd is as follows: △ c1bd is equilateral triangle with side length √ 2a and area √ 3 / 2A & sup2;, and the distance can be calculated as √ 3 / 3a