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Unit 10-Day 3 Rectangles: Objective: Finding the Perimeter & Area of a rectangle

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Rectangles: Opposite sides are congruent. All angles are right angles.

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Perimeter: w w l l P = l + w + l + w P = 2 l + 2 w Formula:

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Example #1: Find the perimeter of a rectangle with the side length of 12 inches and a width length of 5 inches. 5 in. 12 in. P = 2(12) + 2(5) P = 24 + 10 P = 34 in. P = 2 l + 2 w

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EXAMPLE #2 x x+5 The perimeter of the rectangle is 26 inches. Find x. P = 2l + 2w 26 = 2(x+5) + 2(x) 26 = 2x + 10 + 2x 26 = 4x + 10 16 = 4x -10 x = 4

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AREA: A = (length)(width) A = l w l w Formula Area of a Rectangle: w l

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Example #3: Find the area of the rectangle. 8 in 12 in A = l w A = (12)(8) A = 96 in. 2

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EXAMPLE #4: 10 6 5 7 Find the area of the shaded region.

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Practice #2: The area of a rectangle is 50 cm 2. The length is 2x and the width is x. What is the perimeter? P = 30 cm.

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Day 4: Rectangular Prism Surface Area and Volume

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Rectangular Prism: A three-dimensional figure that has 6- faces that are rectangles. Height Length Width

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Surface Area of a Rectangular Prism: Formula: S.A. = + + 2LW2LH2WH Formula: SA = 2LW+2LH+2WH length width height

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Example #1: Find the surface area of a rectangular prism with a height of 5, a length of 10, & a width of 4. 5 10 4 SA = 2LW + 2LH + 2WH SA = 2(10)(4)+2(10)(5)+2(4)(5) SA = 80 +100 + 40 SA = 220 units 2

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Practice #1: Find the surface area of a rectangular prism with a height of 2, a length of 15, & a width of 3. 2 15 3 SA = 2LW + 2LH + 2WH SA = 2(15)(3)+2(15)(2)+2(3)(2) SA = 90 +60 + 12 SA = 162 units 2

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Volume: Definition: The measure in cubic units of the interior of a solid figure; or the space enclosed by a solid figure. Ex. How much sand will it hold?

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Volume of a Rectangular Prism: FORMULA: Volume: length x width x height

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Example #2: Find the volume of the rectangular prism. 15 5 3 Volume = l w h = (15)(5)(3) = 225 units 3

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Example #3: Find the side lengths of the rectangular prism with a volume of 512 in. 3 4x 2x x Volume = l w h 512 = (4x)(2x)(x) 512 = 8x 3 8 8 64 = x 3 x = 4 4 16 8

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Practice #2: 1.Find the volume of a rectangular prism with a length of 6, height of 4, and width of 3. 2.Find the side lengths of a rectangular prism with a volume of 1500 cm 3. 2x 3x 2x x = 5 l = 15 h = 10 w = 10 V = 72 units 3

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