The area of triangle ABC is 2. Find the area of the section of the pyramid ABCD by the plane passing through

| January 1, 2021 | education

The area of triangle ABC is 2. Find the area of the section of the pyramid ABCD by the plane passing through the midpoints of the edges AD, BD, CD.

Consider triangles ABS and A1B1S. These triangles are similar in common angle and parallel straight lines A1B1 and AB. A1B1 is the middle line of the ABS triangle, as it bisects the sides. Let’s find the coefficient of similarity of triangles A1B1S and ABS.
K = SA1 / SA = 1 / 2. Therefore, A1B1 / AB = 1 / 2. Similarly, considering the other sides of the pyramid, we find that triangles A1B1C1 and ABC are similar with the coefficient of similarity K = 1/2.
Then the ratio of the areas of similar triangles is equal to the square of the similarity coefficient.
S1 / S = (1/2) 2 = 1/4.
S1 = 2 * (1/4) = 1/2.
Answer: The cross-sectional area is 1/2 cm2.



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