Question

name date period lesson 11 - 12: polyhedra and nets cool down: unfolded 1. what kind of polyhedron can be assembled from this net? 2. find the surface area (in square units) of the polyhedron. show your reasoning.

Explanation:

Step1: Identify the polyhedron

The net can be folded into a rectangular - prism. Each square in the net represents a face of the polyhedron.

Step2: Count the number of unit - squares on each face

Let's assume the dimensions of the rectangular - prism formed. By observing the net, we can see the possible dimensions. Suppose the length $l = 4$, width $w = 3$, and height $h = 2$.
The surface area formula of a rectangular - prism is $SA=2(lw + lh+wh)$.
$lw=4\times3 = 12$, $lh = 4\times2=8$, $wh=3\times2 = 6$.

Step3: Calculate the surface area

$SA = 2(12 + 8+6)$
$SA=2\times(26)$
$SA = 52$ square units.

Answer:

1. The polyhedron is a rectangular - prism.
2. The surface area of the polyhedron is 52 square units.