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Published byArturo Stanwick Modified about 1 year ago

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How can you determine the amount of paint needed to cover the walls of your bedroom - but not the door, windows, and ceiling?

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In this lesson you will learn how to solve real-life problems by applying your knowledge of surface area.

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Let’s Review Surface area is the sum of the areas of the faces on a 3D solid.

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A Common Mistake In real-life situations, sometimes we do not need to find the areas of all of the faces on a particular 3D solid. What if I need to paint my bedroom? floor and ceiling door and window

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Core Lesson Katy is painting the walls of her bedroom, shown below. Katy will not paint the floor, the ceiling, or the door. Katy’s door is 3 feet x 8 feet. If one quart of paint covers 100 square feet, how many quarts will Katy need to purchase? SA = 2 (Sm. Wall) + 2 (Lg. Wall) - Door 12 feet 8 feet 10 feet = 2 (L W) + 2 (L W) - (L W) = 2 (8 10) + 2 (12 10) - (3 8) = 2 (80) + 2 (120) - (24) = 160 + 240 - 24 There are 376 square feet of wall that need to be covered, so Katy must purchase 4 quarts of paint.

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In this lesson you have learned to solve real-life problems by applying your knowledge of surface area.

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Guided Practice The dimensions of Bria’s camping tent are shown below. The tent is not waterproof, so Bria wants to put a tarp over it, in case it rains. The tarp will cover two of the tent’s rectangular faces. Which size tarp should she buy - the one that is 50 feet 2, 100 feet 2, or 150 feet 2. 6 feet 7 feet 5 feet 4 feet SA = 2 (Rectangle) = 2 (L W) = 2 (7 5) = 2 (35) = 70 ft 2 Bria should buy the 100 feet 2 tarp.

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Extension Activities The house to the right is in need of a new roof. How many square feet of shingles must be purchased? Roofing is measured in “squares.” A square is equal to 100 square feet of roofing. How many squares must be purchased? A square costs $65. How much will the new roofing cost? 20 feet 60 feet 7 feet

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Extension Activities A website sells value rolls of wrapping paper and advertises that, “The most popular size is 25 inches by 405 inches, which can wrap approximately 175 - 200 gifts.” How many square feet of wrapping paper are on one roll? According to this website, what is the surface area of an average gift? If the roll costs $40, about how much does it cost to wrap one gift?

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Quick Quiz Renata bought a package of candy to give to her friend as a gift. The candy is shaped like a triangular prism, with the dimensions, below. She has three different sizes of wrapping paper to choose from. Which will be the best for wrapping the candy — the paper that is 80 cm 2, 130 cm 2, or 180 cm 2 ? Cereal boxes have the dimensions indicated in the illustration, to the left. The cereal box factory is about to close for the weekend, and there are just 1,000 in 2 of cardboard left. How many more cereal boxes can be produced at the factory with the remaining cardboard?

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