The height of the pyramid is divided into four equal parts and planes parallel to the base

| March 2, 2021 | education

The height of the pyramid is divided into four equal parts and planes parallel to the base are drawn through the division points. The base area is 400 sq. units Determine the area of the resulting sections.

Let the height of the pyramid be h cm.

The sections of the pyramid divide the original one into three more pyramids, which are similar to each other and similar to the original pyramid.

The height of the first pyramid, processed by the section, is h * 3/4 ​​cm.

Then K = h / (h * 3/4) = 4/3.

Then S / S1 = K ^ 2 = 16/9.

S1 = 9 * S1 / 16 = 400 * 9/16 = 225 cm2.

The height of the second pyramid, processed by the section, is h * 1/2 cm.

Then K = h / (h * 1/2) = 2/1.

Then S / S2 = K ^ 2 = 4/1.

S2 = 9 * S1 / 16 = 400 * 1/4 = 100 cm2.

The height of the second pyramid, processed by the section, is h * 1/4 cm.

Then K = h / (h * 1/4) = 4/1.

Then S / S3 = K ^ 2 = 16/1.

S3 = 9 * S3 / 16 = 400 * 1/16 = 25 cm2.

Answer: The cross-sectional areas are 225 cm2, 100 cm2, 25 cm2.



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