Transcript Document
How do you calculate the exact amount of wrapping paper needed to wrap a shoe box? In this lesson you will learn how to find the surface area of a rectangular prism by analyzing the prism’s six faces, and computing their areas. Let’s Review Surface area is the sum of the areas of the faces on a 3D solid. Let’s Review We find the area of a rectangle by multiplying its length (L) by its width (W). rectangle area = length • width A=L•W Core Lesson What is the surface area of this rectangular prism? 6 in. 8 in. 3 in. 6 in. 8 in. 3 in. 8 in. 6 3 in. Core Lesson Rec. Prism SA = 2(sm. rec.) + 2 (med. rec.) + 2(lg. rec.) = 2 (L • W) + 2 (L • W) + 2 (L • W) = 2 (3 • 6 ) + 2 (3 • 8) + 2 (6 • 8) = 2 (18) + 2 (24) + 2 (48) = 36 + 48 + 96 6 in. 8 in. 3 in. This rectangular prism has a surface area of 180 square inches (or 180 in2). Core Lesson What is the surface area of this cube? 5 cm. Core Lesson Rec. Prism SA = 6 (square) = 6 (s2) = 6 (52) = 6 (25) 5 cm. This cube has a surface area of 150 square centimeters (or 150 cm2). In this lesson you have learned how to find the surface area of a rectangular prism by analyzing the prism’s six faces, and computing their areas. Guided Practice What is the surface area of this rectangular prism? 2in. 10 in. 2 in. Guided Practice Rec. Prism SA = 2 (square) + = 2 (L • W) = 2 (2 • 2 ) = 2 (4) = 8 2in. 10 in. 2 in. + + + + 4 (lg. rec.) 4 (L • W) 4 (10 • 2 ) 4 (20) 80 This rectangular prism has a surface area of 88 square inches (or 88 in2). Extension Activities Find a box, and measure its side lengths. Use this information to determine precisely how much tin foil you will need to cover all of the box’s surfaces. Once you’ve found your answer, ask your teacher for exactly the correct amount of foil needed to cover the surfaces, with no extra paper. Were your computations correct? Why or why not? Extension Activities Can you think of two different rectangular prisms that have the same surface area? What are their dimensions? Be prepared to explain how you found your answer. Quick Quiz What is the surface area of this prism? 7 ft 6 ft 2 ft How many square yards of paper would be needed to wrap this cube? 10 yd