Question

practice problems 6 from unit 1, lesson 14 a. what polyhedron can be assembled from this net? b. what information would you need to find its surface area? be specific, and label the diagram as needed.

Explanation:

Step1: Identify the polyhedron

The net consists of 2 congruent triangular faces and 3 rectangular faces. This is the net of a triangular prism.

Step2: Determine surface - area information

The surface area of a triangular prism is the sum of the areas of its faces. For the three rectangular faces, we need the lengths and widths of the rectangles. Let the lengths of the rectangles be \(l_1\), \(l_2\), \(l_3\) and the widths be \(w_1\), \(w_2\), \(w_3\) (in this case, some of the widths may be equal). For the two triangular faces, we need the base \(b\) and height \(h\) of the triangle.

Answer:

a. Triangular prism
b. For the rectangular faces: lengths and widths of the rectangles; for the triangular faces: base and height of the triangle.