A plane is drawn through the vertex A1 and the midpoints of the edges AC and BC of the regular
| March 5, 2021 | education
A plane is drawn through the vertex A1 and the midpoints of the edges AC and BC of the regular triangular prism ABCA1B1C1. Determine the type of section and find its perimeter if the side of the base of the prism is 8 cm and the side edge is 3 cm.
The desired section is the isosceles trapezoid A1B1MK, in which A1B1 = 8 cm, KM = AB / 2 = 8/2 = 4, since KM is the middle line of the right triangle ABC.
A1K = B1M as hypotenuse of equal right-angled triangles.
From the right-angled triangle АА1К, according to the Pythagorean theorem, we determine the length of the hypotenuse А1К.
A1K ^ 2 = AA1 ^ 2 + AK ^ 2 = 9 + 16 = 25.
A1K = 5 cm.
Then the perimeter of the section is: P = 5 + 5 + 8 + 4 = 22 cm.
Answer: The perimeter of the section is 22 cm.
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