The height of a regular rectangular truncated pyramid is 4 cm, and the diagonal is 5 cm. Find the area of the diagonal section.
| June 12, 2021 | education
The diagonal section of a regular truncated pyramid is an isosceles trapezium АА1С1С.
The diagonal AC1 of the pyramid is also the diagonal of the axial section, and the height OO1 of the pyramid is also the height of the C1H trapezoid.
The diagonal and the height form a right-angled triangle AC1H, in which, according to the Pythagorean theorem, we determine the length of the segment AH.
AH ^ 2 = AC1 ^ 2 – C1H ^ 2 = 25 – 16 = 9.
AH = 3 cm.
By the property of an isosceles trapezoid, the length of the segment AH, cut off by the height, is equal to the length of the middle line of the trapezoid.
Then Strap = AH * C1H = 3 * 4 = 12 cm2.
Answer: The area of the diagonal section is 12 cm2.
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