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Wrapping Up Geometry

Wrapping Up Geometry. Lesson 2 of 3. Wrapping Up Geometry – Surface Area. Learning Objective: Today we will explore how to represent triangular prisms using nets and find the surface area of a triangular prism. top. top. back. front side. back side. bottom. bottom.

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Wrapping Up Geometry

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  1. Wrapping Up Geometry Lesson 2 of 3

  2. Wrapping Up Geometry – Surface Area Learning Objective:Today we will explore how to represent triangular prisms using nets and find the surface area of a triangular prism. top top back front side back side bottom bottom

  3. Surface Area…when you think about the words surface and area and put them together… = + + + +

  4. QUICK WRITE Silently, in your own words, describe what the diagram means in terms of a definition of surface area. = + + + +

  5. Let’s take a look at what finding the surface area means in a triangular prism… 11 inches 6 inches 14 inches 7 inches 14 inches The bases of the triangular prism are the…triangles (we name prisms after their base shapes.) We know which faces are the bases because they are congruent to each other and parallel to each other. The lateral faces of the triangular prism are…rectangles (prism faces are ALWAYS rectangles.)

  6. When you create the net, label each face as a base or lateral face, then with the correct measures. lateral face 14 inches 11 inches 11 inches 7 inches 6 inches lateral face base base 7 inches 14 inches lateral face

  7. Break the net down into the sum of its parts… 14 inches 11 inches + 7 inches LATERALFACES 6 inches + BASES + 6 inches 7 inches + 11 inches 14 inches 6 inches 7 inches

  8. Break the prism down into the sum of its faces by looking at the net’s area…start with the base area The formula for the area of a triangle is: 11 inches 6 inches There are two triangles in the net, so 2A = 66 in2

  9. Then find the lateral face areas… The area for a rectangle is: 14 inches There are two rectangles this size, so 7 inches 6 inches 7 inches The faces on the side (lateral faces) sum to 238 in2

  10. Find the sum of the base areas and the lateral face areas… 33 in2 + 98 in2 LATERALFACES + BASES + 42 in2 + 33 in2 66 in2 +238 in2 98 in2 Surface Area =304 in2

  11. Now you try it… • Sketch a 2-D net of this 3-D triangular prism and label the measures of each face correctly. • Identify the bases and lateral faces.

  12. From Prism to Net… 11 cm 20 cm 18 cm 16 cm 18 cm 15 cm base 15 cm 15 cm 20 cm 18 cm 11 cm 11 cm 11 cm 15 cm base bottom right face left face 18 cm

  13. Find each face’s area, then sum them up… 135 cm2 135 cm2 198 cm2 198 cm2 +165 cm2 831 cm2 18 cm 135 cm2 15 cm 15 cm 20 cm 18 cm 198 cm2 165 cm2 11 cm 11 cm 11 cm 198 cm2 15 cm 135 cm2 18 cm

  14. Wrap Up Surface Area of Triangular Prisms • Break the prism into the sum of the area of its faces • Sketch a net of the prism • Compute the area of each prism face • Sum up the areas of each face

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