The diagonal AC of the base of the regular quadrangular pyramid SABCD is 6.
August 6, 2021 | education
| The diagonal AC of the base of the regular quadrangular pyramid SABCD is 6. The lateral edge SB is 5. Find the height of the pyramid SO.
Since a regular quadrangular pyramid SABCD is given, there is a square at its base, and equal triangles are its side faces. Consider an isosceles triangle SAC obtained in a diagonal section. From the condition of the problem it is known that the diagonal AC of the base is 6, the lateral edge SB = 5, then SA = 5. The height of the SO triangle will simultaneously be the height of the pyramid, we find it from the right-angled triangle ASO by the Pythagorean theorem: SA² = SO² + AO², where AO = AC / 2 = 6/2 = 3. We get the equation: 5² = SO² + 3²; SO = 4.
Answer: The height of the pyramid is 4.
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