In a regular 4-sided pyramid, the height = 12cm and the height of the side edge = 15cm. Find the side edge of the pyramid.
| August 1, 2021 | education
Let’s draw the segment OH.
The triangle MOH is rectangular, then, according to 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.
Point O is the middle of the AC diagonal, then OH is the middle line of the ACD triangle, and therefore AD = CD = 2 * OH = 2 * 9 = 18 cm, then CH = CD / 2 = 18/2 = 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.
MС = √306 = 3 * √34 cm2.
Answer: The length of the side rib is 3 * √34 cm2.
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