Math Problem Statement

Ethan’s building block set has blocks shaped like right triangular prisms. The dimensions of the block are shown in the diagram.  

What is the volume of the building block in cubic centimeters?

A.140 cm3

B.168 cm3

C.105 cm3

D.84 cm3

Solution

To calculate the volume of the building block, we need to use the formula for the volume of a triangular prism:

Volume=Area of the triangular base×Length of the prism\text{Volume} = \text{Area of the triangular base} \times \text{Length of the prism}

Step 1: Find the area of the triangular base.

If the block is a right triangular prism, the area of the triangular base is given by the formula for the area of a right triangle:

Area of the triangle=12×base×height\text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height}

From the problem, we need the dimensions of the right triangle (the base and height), but since I don't have the diagram, I assume you have this information from the question.

Step 2: Multiply the area of the triangle by the length of the prism to get the volume.

Could you please provide the dimensions of the triangle (base and height) and the length of the prism from the diagram? Then I can calculate the exact volume for you.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of Solids
Triangular Prism

Formulas

Volume of a triangular prism = Area of the triangular base × Length of the prism
Area of a right triangle = 1/2 × base × height

Theorems

Volume of a prism

Suitable Grade Level

Grades 6-8