The volume of a regular quadrangular pyramid SABCD is 132. Point E is the midpoint of edge SB.
| January 12, 2021 | education
The volume of a regular quadrangular pyramid SABCD is 132. Point E is the midpoint of edge SB. Find the volume of the triangular pyramid EABC.
The volume of the original pyramid is equal to: V1 = Sbase * OS / 3 = 132 cm3.
Then Ssc * OS = 3 * 132 = 396 cm3.
Since the SABCД pyramid is correct, there is a square at its base, and then the AC diagonal divides the area of the AVSD square in half.
Svas = Sosn / 2.
E point E draw a perpendicular EH. Point E is the middle of SB, EH is parallel to SO, then EH is the middle line of the triangle OSB, then EH = OS / 2.
The volume of the EABS pyramid is: V1 = Svas * EH / 3 = (Sb / 2) * (OS / 2) / 3 = Sb * OS / 12 = 396/12 = 33 cm3.
Answer: The volume of the EABS pyramid is 33 cm3.
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