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Calculate Volume of a Right Triangular Prism with Given Dimensions
Mathematics
Grade 10 of Junior High School
Question Content
Determine the volume of the right triangular prism. (Lines that appear perpendicular are perpendicular.) The prism has a right triangular base with legs 5 cm and 12 cm, and the length of the prism is 13 cm.
Correct Answer
390 cm³
Detailed Solution Steps
1
Step 1: Recall the volume formula for a prism: $V = Bh$, where $B$ is the area of the base, and $h$ is the length (height) of the prism.
2
Step 2: Calculate the area of the right triangular base: $B = \\frac{1}{2} \\times base \\times height = \\frac{1}{2} \\times 5 \\times 12 = 30$ cm².
3
Step 3: Substitute $B=30$ cm² and the prism length $h=13$ cm into the volume formula: $V = 30 \\times 13 = 390$ cm³.
Knowledge Points Involved
1
Prism Volume Formula
The volume of any prism is given by $V = Bh$, where $B$ is the area of the prism's base (any polygon shape) and $h$ is the perpendicular distance between the two bases (also called the length of the prism). It applies to all right and oblique prisms.
2
Area of a Right Triangle
The area of a right triangle is calculated as $\\frac{1}{2} \\times leg_1 \\times leg_2$, where the two legs are the sides that form the right angle. This is a special case of the general triangle area formula $\\frac{1}{2} \\times base \\times height$, using the two legs as the base and height since they are perpendicular.
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