In a regular quadrangular pyramid, the height is 12 cm, and the height of the side edge is 15 cm. Find the side edge.
| May 6, 2021 | education
The height of the side face and the height of the pyramid form a right-angled triangle HOM.
Then, by the Pythagorean theorem, OH ^ 2 = MH ^ 2 – MO ^ 2 = 225 – 144 = 81. OH = 9 cm.
The side faces of the pyramid are equilateral triangles, then the height of MH is its median, and then DH = CH.
In the right-angled triangle COH, the acute angles are 45, then the triangle COH is rectangular and isosceles, OH = CH = 9 cm.
In a right-angled triangle MCH, according to the Pythagorean theorem, we determine the length of the hypotenuse MC.
MC ^ 2 = MH ^ 2 + CH ^ 2 = 225 + 81 = 306.
MC = √306 = 3 * √34 cm2.
Answer: The length of the side rib is 3 * √34 cm2.
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