At the base of the straight prism there is an isosceles trapezoid with bases equal to 10 cm and 22 cm

| September 11, 2021 | education

At the base of the straight prism there is an isosceles trapezoid with bases equal to 10 cm and 22 cm, as well as with a height equal to 12 cm. A section is drawn through the diagonal of the trapezoid perpendicular to the base of the prism. Determine its area if the volume of the prism is 1920 cm.

In an isosceles trapezoid, the CH height divides the larger base into two segments, the larger of which is equal to half the sum of the base lengths. AH = (BC + AD) / 2 = (10 + 22) / 2 = 16 cm.

Then AC ^ 2 = AH ^ 2 + CH ^ 2 = 256 + 144 = 400.

AC = 20 cm.

Determine the area of the base of the prism.

Sb = (ВС + АD) * СН / 2 = (10 + 22) * 12/2 = 192 cm2.

Knowing the volume and area of the base, we determine the height of the prism.

V = Sosn * AA1.

1920 = 192 / AA1.

AA1 = 1920/192 = 10 cm.

The sectional area is a rectangle АА1С1С, then Ssection = АА1 * АС = 10 * 20 = 200 cm2.

Answer: The cross-sectional area is 200 cm2.



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