A plane parallel to the base of the pyramid divides its height by a ratio of 1: 2

| September 3, 2021 | education

A plane parallel to the base of the pyramid divides its height by a ratio of 1: 2 Calculate the cross-sectional area if it is less than the base area by 24 cm ^ 2

Let us denote the cross-sectional area through S1, and the base area through S, H – the height of the pyramid, h – the height drawn from the top of the pyramid to a plane of parallel section.

Then, by the problem statement, the ratio (H – h) / h = 2; S1 + 24 = S.

From the ratio (H – h) / h = 2 we have, (H – h) = 2h → H = 3h.

It is known that the areas of such polygons are equal to the square of the ratio of heights, which means we have the following equality:

S / S1 = (H / h) ^ 2 = (3h / h) ^ 2 = 3 ^ 2 = 9 → S = 9S1. Substitute the found in S1 + 24 = S.

S1 + 24 = 9S1 → 24 = 9S1 – S1 → 24 = 8S1 → S1 = 24/8 = 3 cm2.



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