Find the volume of a right triangular prism whose altitude is 3m and a right triangular base whose legs are 1m and 2m
The Correct Answer and Explanation is:
Correct Answer:
The volume of the right triangular prism is 3 cubic meters (m³).
Textbook-Style Explanation
To calculate the volume of a right triangular prism, the following formula is used:Volume=Area of base×Height (or length/altitude) of the prism\text{Volume} = \text{Area of base} \times \text{Height (or length/altitude) of the prism}Volume=Area of base×Height (or length/altitude) of the prism
A right triangular prism is a three-dimensional figure with two congruent right triangle bases and three rectangular lateral faces. The given problem states that the base is a right triangle with legs of 1 meter and 2 meters, and the altitude (height) of the prism (the distance between the two triangular bases) is 3 meters.
Step 1: Calculate the Area of the Triangular Base
The base of the prism is a right triangle. The formula for the area AAA of a right triangle is:A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}A=21×base×height
Here, the legs of the triangle are 1 meter and 2 meters, which serve as the base and height:A=12×1×2=22=1 m2A = \frac{1}{2} \times 1 \times 2 = \frac{2}{2} = 1 \, \text{m}^2A=21×1×2=22=1m2
Step 2: Multiply the Area of the Base by the Altitude of the Prism
The prism has an altitude (length/depth) of 3 meters:Volume=1 m2×3 m=3 m3\text{Volume} = 1 \, \text{m}^2 \times 3 \, \text{m} = 3 \, \text{m}^3Volume=1m2×3m=3m3
Final Answer:
3 m3\boxed{3 \, \text{m}^3}3m3
This means the total space occupied by the triangular prism is 3 cubic meters. Volume is always expressed in cubic units because it measures how much three-dimensional space an object occupies. The right triangular prism here is relatively simple due to the right triangle base, allowing direct application of the basic geometric formulas.
