In a straight quadrangular prism, the base is a rectangle with sides 7 and 24, and the height is 8.
| February 18, 2021 | education
In a straight quadrangular prism, the base is a rectangle with sides 7 and 24, and the height is 8. Find the areas of dioganal sections.
Since there is a rectangle at the base of the prism, its diagonals AC and BD are equal.
In a right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the ВD diagonal.
BD ^ 2 = AB ^ 2 + AD^ 2 = 7 ^ 2 + 24 ^ 2 = 49 + 576 = 625.
BD = 25 cm.
The prism is straight, then the heights of the prism are perpendicular to the base.
The diagonal sections of the prism are equal-sized rectangles АА1С1С and ВВ1D1D.
Determine the cross-sectional area.
Ssection = BB1 * ВD = 8 * 25 = 200 cm2.
Answer: The areas of the diagonal sections are 200 cm2.
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