Question

1. jada drew a net for a polyhedron and calculated its surface area.

a. what polyhedron can be assembled from this net?
b. jada made some mistakes in her area calculation. what were the mistakes?
c. find the surface area of the polyhedron. show your reasoning.

Explanation:

Step1: Identify the polyhedron

The net has two triangular bases and three rectangular lateral faces, so it's a triangular prism.

Step2: Consider possible calculation mistakes

Common errors in area calculations for polyhedra involve formula - use and face - counting.

Step3: Calculate surface area

Sum the areas of all faces of the triangular prism. First, account for the two triangular faces, then add the areas of the three rectangular faces.

Answer:

a. Triangular prism
b. Without knowing Jada's calculations, it's hard to say exactly. But possible mistakes could be incorrect use of area - formulas for rectangles or triangles, or double - counting or missing some faces.
c.

1. Analyze the faces:

• The net has two congruent triangular faces and three rectangular faces.
• For the triangular faces: The area of each triangular face is \(A_{triangle}= 12\space cm^{2}\).
• For the rectangular faces: The areas are \(A_1 = 20\space cm^{2}\), \(A_2=16\space cm^{2}\), \(A_3 = 12\space cm^{2}\).

1. Calculate the surface area \(S\):

• The surface area of a polyhedron is the sum of the areas of all its faces.
• \(S=2\times A_{triangle}+A_1 + A_2+A_3\).
• Substitute the values: \(S = 2\times12+20 + 16+12\).
• First, \(2\times12 = 24\).
• Then, \(24+20+16 + 12=(24+20)+(16 + 12)=44+28 = 72\space cm^{2}\).