Triangular prism

Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.

Result

V =  300 cm3

Solution:

a=5 cm h=10 cm S=130 cm2  c=S/h=130/10=13 cm b=c2−a2=132−52=12 cm S2=a⋅ b/2=5⋅ 12/2=30 cm2 V=S2⋅ h=30⋅ 10=300=300 cm3a = 5 \ cm \ \\ h = 10 \ cm \ \\ S = 130 \ cm^2 \ \\ \ \\ c = S/h = 130/10 = 13 \ cm \ \\ b = \sqrt{ c^2-a^2 } = \sqrt{ 13^2-5^2 } = 12 \ cm \ \\ S_{ 2 } = a \cdot \ b/2 = 5 \cdot \ 12/2 = 30 \ cm^2 \ \\ V = S_{ 2 } \cdot \ h = 30 \cdot \ 10 = 300 = 300 \ cm^3

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Following knowledge from mathematics are needed to solve this word math problem:

Pythagorean theorem is the base for the right triangle calculator. Tip: Our volume units converter will help you with the conversion of volume units. See also our trigonometric triangle calculator.

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