Quadrilateral oblique prism

What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°.

Correct answer:

V = 1.0113 m³

Step-by-step explanation:

a = 1 m b = 1.1 m c = 1.2 m d = 0.7 m h = 3.9 m φ = 20 + 35 / 60 = \frac{2 4 7}{1 2} ≐ 20.5833^{\circ} β = 50.5^{\circ} u^{2} = a^{2} + b^{2} - 2 \cdot a \cdot b \cdot cos β u = a^{2} + b^{2} - 2 \cdot a \cdot b \cdot cos β = a^{2} + b^{2} - 2 \cdot a \cdot b \cdot cos 50.5 ° = 1^{2} + 1 . 1^{2} - 2 \cdot 1 \cdot 1.1 \cdot cos 50.5 ° = 1^{2} + 1 . 1^{2} - 2 \cdot 1 \cdot 1.1 \cdot 0.636078 = 0.90035 m s = (a + b + u) / 2 = (1 + 1.1 + 0.9003) / 2 ≐ 1.5002 m S_{1} = s \cdot (s - a) \cdot (s - b) \cdot (s - u) = 1.5002 \cdot (1.5002 - 1) \cdot (1.5002 - 1.1) \cdot (1.5002 - 0.9003) ≐ 0.4244 m s_{2} = (c + d + u) / 2 = (1.2 + 0.7 + 0.9003) / 2 ≐ 1.4002 m S_{2} = s_{2} \cdot (s_{2} - c) \cdot (s_{2} - d) \cdot (s_{2} - u) = 1.4002 \cdot (1.4002 - 1.2) \cdot (1.4002 - 0.7) \cdot (1.4002 - 0.9003) ≐ 0.3132 m h_{2} = h \cdot sin φ = h \cdot sin 20.583333333333 ° = 3.9 \cdot sin 20.583333333333 ° = 3.9 \cdot 0.351569 = 1.37112 m S = S_{1} + S_{2} = 0.4244 + 0.3132 ≐ 0.7376 m V = S \cdot h_{2} = 0.7376 \cdot 1.3711 = 1.0113 m^{3}

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You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

volume

Grade of the word problem:

high school

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