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The problem involves determining distances from specific points to planes within a cube. Here's how we can approach it:

We are given a cube \( ABCD.EFGH \) with a side length of 16 cm. Let’s break down each part of the problem step by step.

### 1. Distance from point \( B \) to plane \( ABFE \)
- Plane \( ABFE \) is one of the faces of the cube containing points \( A, B, F, E \).
- Since point \( B \) lies on this plane, the distance from \( B \) to this plane is 0 cm.

### 2. Distance from point \( B \) to plane \( DCGH \)
- Plane \( DCGH \) is the opposite face of the cube from \( ABFE \). It is parallel to the plane \( ABFE \).
- The distance between two parallel planes in a cube is the length of the cube’s edge, which is 16 cm. Therefore, the distance from point \( B \) to plane \( DCGH \) is 16 cm.

### 3. Distance from point \( C \) to plane \( BDG \)
- Plane \( BDG \) passes through points \( B, D, G \), forming a diagonal plane of the cube.
- To find the distance from point \( C \) to this plane, we calculate the perpendicular distance from point \( C \) to the diagonal plane. This involves more advanced geometry, but since the cube is symmetric, the answer typically involves a formula based on the cube's side length. Here, the result is \( \frac{16}{\sqrt{3}} \) cm, the perpendicular distance from any point in the cube to a diagonal plane.

### 4. Distance from point \( C \) to plane \( BDE \)
- Plane \( BDE \) passes through points \( B, D, E \). This forms another diagonal plane within the cube.
- The distance from point \( C \) to this plane can also be calculated geometrically, similar to the previous case, resulting in \( \frac{16}{\sqrt{3}} \) cm.

### 5. Distance from point \( C \) to plane \( MNO \)
- Here, points \( M, N, O \) are defined as midpoints of the edges \( BC \), \( CD \), and \( CG \), respectively.
- The plane \( MNO \) is determined by these three midpoints. To find the distance from point \( C \) to this plane, we again need to calculate the perpendicular distance from \( C \) to the plane formed by these midpoints. The calculation involves the symmetry and midpoints of the cube, which leads to a distance of \( \frac{16}{2} = 8 \) cm.

### Summary of Distances:
1. Distance from point \( B \) to plane \( ABFE \): 0 cm.
2. Distance from point \( B \) to plane \( DCGH \): 16 cm.
3. Distance from point \( C \) to plane \( BDG \): \( \frac{16}{\sqrt{3}} \) cm.
4. Distance from point \( C \) to plane \( BDE \): \( \frac{16}{\sqrt{3}} \) cm.
5. Distance from point \( C \) to plane \( MNO \): 8 cm.

Would you like a detailed explanation on any of these steps or calculations?

### Related Questions:
1. What is the formula for the distance from a point to a plane in 3D geometry?
2. How can we calculate the distance between two parallel planes in a cube?
3. What is the geometric significance of a diagonal plane in a cube?
4. How does symmetry help in solving 3D geometry problems involving cubes?
5. How would the solution change if the cube had a different side length?

### Tip:
When working with geometry in cubes, understanding symmetry and parallel planes can simplify complex distance calculations.

Diketahui sebuah kubus ABCD.EFGH dengan panjang rusuk 16 cm, tentukan: 
1. Jarak dari titik B ke bidang ABFE 
2. Jarak dari titik B ke bidang DCGH 
3. Jarak dari titik C ke bidang BDG 
4. Jarak dari titik C ke bidang BDE 
5. Jika titik M, N, dan O berturut turut berada pada tengah garis BC, CD, dan CG maka tentukan jarak dari titik C ke bidang MNO

This problem involves calculating distances from points to various planes in a cube with a side length of 16 cm. Learn to solve for distances using 3D geometry formulas and symmetry, including the distance from point B to planes ABFE and DCGH, and from point C to diagonal planes BDG, BDE, and MNO.

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