Math Problem Statement
Find the volume of each figure
Solution
The figure in the image appears to be a triangular prism, which consists of a triangular base and a rectangular face extended through the height of the prism.
To find the volume of a prism, you can use the following formula:
where:
- is the volume,
- is the area of the base (in this case, the triangle),
- is the height or length of the prism (which is along the 20 cm edge).
Let's break it down:
-
Calculate the area of the triangular base: The base of the triangle is 9 cm, and the height of the triangle (perpendicular to the base) is 4 cm. The area of a triangle is given by:
-
Find the height/length of the prism: The length (or height) of the prism is given as 20 cm.
-
Calculate the volume: Now, multiply the area of the triangular base by the length of the prism:
Thus, the volume of the triangular prism is 360 cubic centimeters (cm³).
Do you want more details or have any further questions?
Here are some related questions you might find helpful:
- How do you find the surface area of a triangular prism?
- What is the difference between a prism and a pyramid?
- How does the Pythagorean theorem help in solving problems involving right triangles?
- How would the volume change if the length of the prism was doubled?
- Can you explain the relationship between base area and height in calculating volume?
Tip: Always verify whether the triangle is right-angled; this simplifies calculations using standard area formulas.
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume of Prisms
Formulas
Volume = Base Area × Height
Theorems
Area of a Triangle
Suitable Grade Level
Grades 6-8
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