1. How do you calculate the exact amount of material used to create this tent?

2. In this lesson you will learn how to find the surface area of a triangular prism by analyzing the prism’s faces, and computing their areas.

3. Let’s Review We find the area of a triangle by multiplying its base by its height, and then cutting that product in half. base height 4 in 6 in Rec. Area = (4 x 6) = 24 in 2 Tri. Area = (4 x 6) / 2 = 12 in 2

4. Core Lesson Surface area is the sum of the areas of the faces on a 3D solid.

5. What is the surface area of this triangular prism? 10 cm 2 cm 7 cm 6 cm 2 cm 6 cm 10 cm 2 cm 10 cm 6 cm

6. Core Lesson Tri Prism SA = 2 (tri.) + (sm. rec.) + 2 (lg. rec.) = 2 ( ) + ( ) + 2 ( ) = 2 (6) + (20) + 2 (70) = 12 + 20 + 140 10 210 7 This triangular prism has a surface area of 172 square centimeters (or 172 cm 2 ). = 2 ( ) + (L W) + 2 (L W) 6 cm 2 cm 10 cm 7 cm

7. In this lesson you have learned how to find the surface area of a triangular prism by analyzing the prism’s faces, and computing their areas.

8. Guided Practice Find the surface area of this triangular prism. (All of the triangle’s sides are congruent.) 5 ft 6 ft 4 ft Tri Prism SA = 2 (tri.) + 3 (rec.) = 2 ( ) + 3 (L W) = 2 ( ) + 3 (4 6) = 30 + 3 (24) This triangular prism has a surface area of 102 square feet. = 30 + 3 (72)

9. Extension Activities This tent, which has a height of 4.5 feet, is designed to comfortably fit three campers. Make an estimate about the size of an average sleeping bag. Use that estimate to determine the approximate surface area of the tent. Compare your answer with that of others in your class.

10. Gina noticed every cube is made of two congruent triangular prisms. She then hypothesized that the cube’s surface area must be twice the surface area of one of the triangular prisms. Is she correct? Explain your answer. = + ?

11. Quick Quiz What is the surface area of this triangular prism? What is the surface area of this prism, with an equilateral triangle base? 3 yd 2.6 yd 4 yd 3 ft 4 ft 5 ft 2 ft