The height of a regular quadrangular pyramid is 10 and the side of the base is 15. Find the length of the apothem of this pyramid.

| January 12, 2021 | education

At the base of a regular quadrangular pyramid lies a square. Its height is lowered to the intersection of the square’s diagonals. The apothem of the side face of the pyramid intersects the side of the square at the point where the perpendicular falls from the point of intersection of the diagonals of the square to the side of the square. According to the properties of a square, the length of this perpendicular is equal to half of its side.
Based on the Pythagorean theorem: x ^ 2 = h ^ 2 + (0.5 * a) ^ 2, where x is the desired apothem, h is the height of the pyramid, a is the side of the square that lies at the base of the pyramid. Substituting the numerical values, we get: x ^ 2 = 100 + 56.25. Having solved this equation, we get x = √ (156.25) = 12.5.
Answer: Apothem is 12.5.



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