Through the height of the trapezoid lying at the base of the straight prism, a section was

| September 12, 2021 | education

Through the height of the trapezoid lying at the base of the straight prism, a section was drawn with an area of 120 cm ^ 2. Determine the volume of the prism if the sides of the trapezoid are 12 cm, 13 cm, 22 cm and 13 cm.

Since the ABCD trapezoid has the sides AB = CD = 13 cm, the ABCD trapezoid is isosceles.

The height BH of the trapezoid ABCD divides its base AD into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases.

AH = (AD – BC) / 2 = (22 – 12) / 2 = 10/2 = 5 cm.

In a right-angled triangle ABH, according to the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2 = 169 – 25 = 144.

BH = 12 cm.

By condition, the cross-sectional area of ​​the BB1H1H is 120 cm2.

Svv1n1n = BH * HH1.

НН1 = Sвв1н1н / ВН = 120/12 = 10 cm.

Determine the area of ​​the base of the prism.

Sb = (ВС + АD) * ВН / 2 = (12 + 22) * 12/2 = 204 cm2.

Let’s define the volume of the prism.

V = Sbn * НН1 = 204 * 10 = 2040 cm3.

Answer: The volume of the prism is 2040 cm3.



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