At the base of the straight prism lies a right-angled triangle with legs of 8 and 6 cm. A plane is drawn through

univerkov | September 13, 2021 | education

At the base of the straight prism lies a right-angled triangle with legs of 8 and 6 cm. A plane is drawn through the larger leg of the lower base and the opposite apex of the upper base of the prism, making an angle of 60 degrees with the plane of the base. Find the cross-sectional area?

Since the prism is straight, its side faces are rectangles. Then triangle ACA1 is rectangular, in which Cos60 = AC / CA1.

CA1 = AC / Cos60 = 6 / (1/2) = 12 cm.

Since a right-angled triangle lies at the base of the prism, the side faces of BCC1B1 and ACC1A1 are perpendicular, and then the section A1CB is a right-angled triangle with a right angle C.

Then Ssec = BC * CA1 / 2 = 8 * 12/2 = 48 cm2.

Answer: The cross-sectional area is 48 cm2.

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