CHAPTER 11 You will need Lateral and Surface • a ruler A • a calculator Area of Right Prisms c GOAL Calculate lateral area and surface area of right prisms. Learn about the Math A prism is a polyhedron (solid whose faces are polygons) whose bases are congruent and parallel. When trying to identify a right prism, ask yourself if this solid could have right prism been created by placing many congruent sheets of paper on prism that has bases aligned one above the top of each other. If so, this is a right prism. Some examples other and has lateral of right prisms are shown below. faces that are rectangles Triangular prism Rectangular prism The surface area of a right prism can be calculated using the following formula: SA 5 2B 1 hP, where B is the area of the base, h is the height of the prism, and P is the perimeter of the base. The lateral area of a figure is the area of the non-base faces lateral area only. When a prism has its bases facing up and down, the area of the non-base faces of a figure lateral area is the area of the vertical faces. (For a rectangular prism, any pair of opposite faces can be bases.) The lateral area of a right prism can be calculated by multiplying the perimeter of the base by the height of the prism. This is summarized by the formula: LA 5 hP. Copyright © 2009 by Nelson Education Ltd. Reproduction permitted for classrooms 11A Lateral and Surface Area of Right Prisms 1 Jorge is trying to wrap a present that is in a box shaped as a right prism. He wants to determine the surface area and lateral area of the prism to see if he has enough wrapping paper to cover the entire box or only the vertical faces of the box. The drawing below shows the dimensions of the present. 1.50 m 1.00 m 0.25 m ? How can Jorge calculate the surface area and lateral area of this right prism? A. Calculate the area of the base of the prism. B. Calculate the perimeter of the base of the prism. C. Use your calculations from parts A and B along with the height of the prism to calculate the total surface area. Use the following formula as a guide for your calculation: SA 5 2B 1 hP. D. Use the formula, LA 5 hP to calculate the lateral area of this prism. E. If Jorge has 1.50 m2 of paper, would he have enough to cover the entire box or only the vertical faces of the box? Reflecting 1. What information do you need to have about a right prism to calculate its surface area? 2. How do the surface area of a prism and the lateral area of a prism differ? 3. Is the lateral area of a right prism ever larger than the surface area? 2 Nelson Mathematics Secondary Year Two, Cycle One Reproduction permitted for classrooms Copyright © 2009 by Nelson Education Ltd. Work with the Math Example 1: Calculating the surface area of a right prism Use the dimensions of the right prism shown below to calculate its surface area. 3.0 cm 3.0 cm 4.0 cm 2.6 cm 3.0 cm Emilio’s Solution First, I will calculate the surface area of this right prism. To do this I must first calculate the area and perimeter of the base of the prism. I will then use the formula SA 5 2B 1 hP to calculate the surface area. The area of the base can be found by using the formula for the area 1 of a triangle, bh. 2 1 (3.0 cm)(2.6 cm) 5 3.9 cm2 2 The perimeter of the base can be found by adding the length of each segment forming the triangular bases. P 5 3.0 cm 1 3.0 cm 1 3.0 cm; P 5 9.0 cm I know the height of this prism is 4.0 cm. I can now substitute the area of the base into the formula for B, the perimeter of the base for P, and the height of the prism for h. I will simplify to determine the total surface area for this right prism. SA 5 2(3.9 cm2) 1 4.0 cm (9.0 cm) 5 43.8 cm2 The surface area is 43.8 cm2. Copyright © 2009 by Nelson Education Ltd. Reproduction permitted for classrooms 11A Lateral and Surface Area of Right Prisms 3 A Checking 6. Determine the surface area of each of 4. Calculate the surface area and lateral the following right prisms. area of the right prism shown. a) 10 mm 15 mm 10 cm 10 mm 2 cm 3 cm B Practising 5. Complete each of the following b) statements with a term that will make 2.00 m 2.00 m it a true statement. a) A is a prism that has bases aligned one above 3.00 m the other and has lateral faces that 1.32 m are rectangles. 3.00 m b) The of a figure is the area of the non-base faces only. c) 12 cm c) The of a 4 cm figure is equal to the height of the prism multiplied by the perimeter of 10 cm its base. d) 3.00 m 3.00 m 1.66 m 5.00 m 5.00 m 4 Nelson Mathematics Secondary Year Two, Cycle One Reproduction permitted for classrooms Copyright © 2009 by Nelson Education Ltd. 7. Determine the surface area and lateral area of each of the following right prisms. a) 1 cm 1 cm 4 cm b) 4.00 mm 4.00 mm 3.00 mm 1.94 mm 7.00 mm c) 14 cm 8 cm 28 cm d) 1 mm 1 mm 11 mm e) 25 cm 9 cm 6 cm Copyright © 2009 by Nelson Education Ltd. Reproduction permitted for classrooms 11A Lateral and Surface Area of Right Prisms 5.