Lateral, Base, Total Surface Area of Pyramids
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Lateral, Base, Total Surface Area of Pyramids
Lesson Plan Launch (10 min) • Students: break down the pyramids into their shapes for base, lateral, and surface areas. Also students take guesses and label the parts of a pyramid. Encourage the students to EDUCATED GUESSES – In a pyramid, is only ONE base with triangular sides that meet at the APEX Presentation (30 min) • (5 min) Debrief # 4 from the launch completely. Make sure to define any words that you feel the students need defined. But “Shade the base and bold the height” (Of the entire shape). Compare this to the slant height and the fact that they are two different heights. Very confusing for students. • (10 min) Relate a 3-D model to a net of a pyramid – Have students sketch the net. Have students even shade the base. This will help students see how to break it down and find base area and lateral area by sketching the net. – This method will also help students not miss a piece. Most common mistake for finding Lateral or surface area is missing a lateral piece. • (15 min) Work through the 2 examples on the next page – Focus on clear solutions. • Point out that the shape of the base always exists in the instructions. i.e. Square base. Practice (15 min) • Students find Lateral, base, and total area of different shapes. Conclusion (10 min) • Real world application of lateral area of a pyramid. – This is a multistep problem. Encourage students to “Size up the problem” before jumping in. Exit Ticket (5 min) Materials • Lesson packets • Exit Tickets • Nets of Pyramids (For remediation for some students) Concept 1. Lateral, Base, Total Surface Area of Pyramids
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Launch
1. What is the shape of the BASE in the pyramid on the left? Sketch it here. 2. What is the shape of the LATERAL pieces on the pyramid on the left? How many are there? Sketch them here. 3. How does the number of LATERAL pieces relate to the number of sides of the BASE?
4. Label the square pyramid below with the following vocabulary words. Make Guesses!!! a) Base edge b) Lateral edge c) Slant height d) Pyramid height e) Apex
Presentation Square Pyramid
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Net of a Pyramid 1. Find the base area, lateral area, and total area of the square pyramid below.
2. Find the base area, lateral area, and total area of the equilateral triangular pyramid below.
Concept 1. Lateral, Base, Total Surface Area of Pyramids
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Practice 1. Find the base area, lateral area, and total area of the square pyramid below.
2. The base edge of the shape below is 12 cm and the slant height is 10 cm. Find the base area, lateral area, and total area of the equilateral triangular pyramid below.
3. Find the base area, lateral area, and total area of the regular hexagonal pyramid below.
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Conclusion The Pyramid of Giza (a square pyramid in Egypt) is one of the 7 wonders of the world. The pyramid is 480 feet high and the slant height is 610 ft. How many square feet of gold would you need to cover the pyramid? If gold costs $120 per square foot, what would be the cost of covering the whole pyramid?
Homework
1. Name the 3-D solid _________________________________________________________ 2. Sketch the net of the shape below. 3. Find the base area (provide a clear solution). 4. Find the lateral area (provide a clear solution). 5. The Luxor hotel and Casino in Las Vegas is a pyramid shaped hotel that is completely made of glass. If the owner wanted to replace ALL the windows in the hotel, would he need to figure out the: base area, lateral area, or surface area? Why? _________________________________________________________ _________________________________________________________ Concept 1. Lateral, Base, Total Surface Area of Pyramids
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Exit Ticket
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