12.2 Nets and Surface Area

1. 12.2 Nets and Surface Area

2. Objectives • Draw 2-dimensional models for 3-dimensional figures • Find surface area

3. Example 1: Sketch a rectangular prism 4 units long, 3 units wide, and 2 units high using isometric dot paper. Step 1 First, we draw the corner of the solid: 2 units down, 4 units to the left, and 3 units to the right.

4. Example 1: Sketch a rectangular prism 4 units long, 3 units wide, and 2 units high using isometric dot paper. Step 2 Next, we draw a parallelogram for the top of the solid.

5. Example 1: Sketch a rectangular prism 4 units long, 3 units wide, and 2 units high using isometric dot paper. Step 3 Now, draw segments 2 units down from each vertex for the vertical edges.

6. Example 1: Sketch a rectangular prism 4 units long, 3 units wide, and 2 units high using isometric dot paper. Step 4 Finally, connect the corresponding vertices. Use dashed lines for the hidden edges. Shade the top of the solid.

7. Example 1: Sketch a rectangular prism 4 units long, 3 units wide, and 2 units high using isometric dot paper. Answer:

8. Nets • If you cut a cardboard box at the edges and lay it flat, you will have a pattern called a net. Nets can be made for most solid figures. What solid figure is this a net for?

9. Example 2: Which net could be folded into a rectangular pyramid if folds are made only along dotted lines?

10. Example 2: Solve the Test ItemA triangular prism has two triangular bases and three rectangular faces. Analyze each answer choice carefully and locate the one that has each of these elements. This net has two triangles for the bases, but only one rectangle. This net has four non-overlapping triangles and a square for the base. It folds into a rectangular pyramid.

11. Example 2: This net has four squares and one triangle. This net has three adjacent rectangles and two triangles. The triangles are adjacent to each of the shorter sides of the middle rectangle. Each base and face of the prism is represented. Answer:B

12. Your Turn: Which net could be folded into a triangular pyramid if folds are made only along the dotted lines? Answer: B

13. Example 3: Use a net to find the surface area of the prism.

14. Example 3: To find the surface area of the prism, add the areas of the three rectangles and the two triangles. Answer: Surface Area = 2(1/2)(4)(1.5) + 2(2.5)(6) + (4)(6) = 60 units2

15. Assignment • Pg. 646 #9, 10, 12, 14 – 23, 28 – 30, 35 - 37