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The plane section ABCD shown in the figure is cut from a cube of edge a. Find the area of this section if D and C are each at the midpoint of an edge.
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| Photo by Math Principles in Everyday Life |
Solution:
The given problem above is asking for the area of a cutting plane ABCD. If C and D are the midpoints of the parallel edges of a cube, then the parallel edges of a cube will bisect into equal parts as shown in the figure below
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| Photo by Math Principles in Everyday Life |
As you notice that there are two right triangles in a cube that are parallel to each other. We need to solve for their hypotenuse using Pythagorean Theorem, as follows
Since AD ║ BC, AB ║ CD, AD ≅ BC, and AB ≅ CD, then quadrilateral ABCD is a rectangle which is a cutting plane. Therefore, the area of a rectangle is
