Question

1. find the total area for the net below.
2. if the net is folded into a polyhedron, what is the name of the polyhedron?

Explanation:

Step1: Identify the shapes in the net

The net consists of 2 congruent triangles and 3 rectangles. Assume the grid - squares have a side - length of 1 unit.

Step2: Calculate the area of the triangles

The base and height of each triangle can be counted from the grid. Let's assume the base of the triangle \(b = 4\) units and height \(h = 3\) units. The area of a triangle is \(A_{\triangle}=\frac{1}{2}bh\). So \(A_{\triangle}=\frac{1}{2}\times4\times3 = 6\) square units. The total area of the two triangles is \(2\times A_{\triangle}=2\times6 = 12\) square units.

Step3: Calculate the area of the rectangles

There are three rectangles. The first rectangle has dimensions \(3\times5\), its area \(A_1 = 3\times5=15\) square units. The second rectangle has dimensions \(4\times5\), its area \(A_2 = 4\times5 = 20\) square units. The third rectangle has dimensions \(5\times5\), its area \(A_3 = 5\times5=25\) square units. The total area of the rectangles is \(A_{rect}=A_1 + A_2+A_3=15 + 20+25=60\) square units.

Step4: Calculate the total area of the net

The total area of the net \(A = 12+60=72\) square units.

Step5: Identify the polyhedron

When the net is folded, it forms a triangular prism. A triangular prism has two triangular bases and three rectangular lateral faces.

Answer:

1. 72 square units
2. Triangular prism