Question

the figure shows a net of a triangular prism. which expression can be used to find the surface area of the prism? 3·4·5; (3 + 4) + (3 + 3) + (3 + 5) + 2(\frac{1}{2} + 3 + 4); (3·4) + (3·3) + (3·5) + \frac{1}{2}(3·4); (3·4) + (3·3) + (3·5) + 2(\frac{1}{2}·3·4)

Explanation:

Step1: Recall Surface Area of Triangular Prism

The surface area of a triangular prism is the sum of the areas of all its faces. A triangular prism has two triangular bases and three rectangular lateral faces. The formula for the area of a triangle is $\frac{1}{2} \times base \times height$, and the area of a rectangle is $length \times width$.

Step2: Identify Faces from the Net

• Triangular Bases: The triangular faces have a base of 3 in and height of 4 in. The area of one triangle is $\frac{1}{2} \times 3 \times 4$, so two triangles would be $2 \times (\frac{1}{2} \times 3 \times 4)$.
• Rectangular Lateral Faces:
• One rectangle has dimensions 3 in (height) and 4 in (length): area $3 \times 4$.
• One rectangle has dimensions 3 in (height) and 3 in (length): area $3 \times 3$.
• One rectangle has dimensions 3 in (height) and 5 in (length): area $3 \times 5$.

Step3: Combine the Areas

Adding the areas of the three rectangles and the two triangles, the surface area expression is $(3 \times 4) + (3 \times 3) + (3 \times 5) + 2 \times (\frac{1}{2} \times 3 \times 4)$, which matches the last option.

Answer:

$(3 \cdot 4) + (3 \cdot 3) + (3 \cdot 5) + 2(\frac{1}{2} \cdot 3 \cdot 4)$ (the last option)