Triangular prism

The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm2 and the body height is 10 cm. Calculate the body volume.

Result

V =  300 cm3

Solution:

a=5 h=10 S3=130 c=S3/h=130/10=13 b=c2−a2=132−52=12 S=a⋅ b/2=5⋅ 12/2=30 V=S⋅ h=30⋅ 10=300 cm3a=5 \ \\ h=10 \ \\ S_{3}=130 \ \\ c=S_{3}/h=130/10=13 \ \\ b=\sqrt{ c^2-a^2 }=\sqrt{ 13^2-5^2 }=12 \ \\ S=a \cdot \ b/2=5 \cdot \ 12/2=30 \ \\ V=S \cdot \ h=30 \cdot \ 10=300 \ \text{cm}^3

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