In a regular triangular pyramid, a section is drawn through the midpoints of three lateral ribs.
| September 23, 2021 | education
In a regular triangular pyramid, a section is drawn through the midpoints of three lateral ribs. Find its area if the edge of the base of the pyramid is 24?
Since points A1, B1 and C1 are the midpoints of the side edges of the pyramid, the segments A1B1, A1C1 and B1C1 are the middle lines of triangles DAB, DAC and DBC.
The length of the median line of the triangle is equal to half the length of the side parallel to it.
A1B1 = AB / 2 = 24/2 = 12 cm, and since triangle ABC is equilateral, A1B1 = A1C1 = B1C1 = 12 cm.
Section A1B1C1 is an equilateral triangle, then Ssection = A1B12 * √3 / 4 = 144 * √3 / 4 = 36 * √3 cm2.
Answer: The cross-sectional area is 36 * √3 cm2.
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