Math Problem Statement
Solution
The solid in the image appears to be a triangular prism. To find both the surface area and the volume of this prism, we need to follow specific formulas based on the dimensions provided.
1. Surface Area of the Triangular Prism:
The surface area of a triangular prism can be calculated using the following formula:
- The base of the prism is a triangle, and its area can be calculated as:
where base = 3.2 cm and height = 2.4 cm.
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The lateral area is the sum of the areas of the three rectangular faces. Each rectangular face has a width equal to the height (or slant) of the prism and a length equal to one of the triangle's sides:
- First side:
- Second side:
- Third side:
So, the lateral area is:
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Math Problem Analysis
Mathematical Concepts
Geometry
Surface Area
Volume
Triangular Prism
Formulas
Surface area of a triangular prism: A = 2 * Base Area + Lateral Area
Base Area of a triangle: (1/2) * base * height
Lateral Area: Sum of areas of three rectangular faces
Volume of a triangular prism: Base Area * height of prism
Theorems
Area formula for triangles
Surface area and volume formulas for prisms
Suitable Grade Level
Grades 6-8
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