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Find the area of a triangle whose vertex is at the midpoint of an upper edge of a cube of edge a and whose base coincides with the diagonally opposite edge of the cube.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
The first thing that we need to do is to solve for the altitude of a triangle first. Since one of the vertex of a triangle is located at the midpoint of the upper edge of a cube, then a triangle is an isosceles triangle. The altitude of an isosceles triangle is equal to the hypotenuse of an isosceles right triangle at the right side of a cube.
By Pythagorean Theorem
Therefore, the area of a triangle is
