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Composite Shapes Math 10-3 Ch.3 Measurement

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Consider a rectangle with the dimensions 2 cm by 3 cm. -What is the perimeter? 2 + 3 + 2 + 3 = 10 cm -What is the area? A rectangle = l x w = 3 x 2 = 6 cm 2

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Let’s now increase the dimensions by a factor of two. The new dimensions are 4 cm by 6 cm -What is the perimeter? 6 + 4 + 6 + 4 = 20 cm -What is the area?l x w = 6 x 4 = 24 cm 2

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Let’s increase the dimensions one more time by two The new dimensions are now 8 cm by 12 cm What is the perimeter? 12 + 8 + 12 + 8 = 40 cm What is the area? l x w = 12 x 8 = 96 cm 2

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Let’s now put this information in a chart: RectangleLengthWidthPerimeterArea Original (#1) 3 cm2 cm10 cm6 cm 2 Original dimension s x 2 (#2) 6 cm4 cm20 cm24 cm 2 Rectangle #2 dimension x 2 (#3) 12 cm8 cm40 cm96 cm 2

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Can you see a pattern forming for the total perimeter of the rectangle? The new perimeter is the old perimeter x 2 Can you see a pattern forming for the area of the rectangle? The new area is the old area x 4 OR x 2 2 If you can’t see the pattern, try dividing the area of rectangle #3 by the area of rectangle #2 96 24 = 4

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Could you predict the perimeter and area for the next rectangle? Perimeter = 40 cm x 2 = 80 cm Area = 96 cm2 x 4 = 384 cm 2 We would say that by increasing the dimensions by two, it increase the perimeter by a factor of 2 and the area by a factor of 4 or by 2 2 !

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Composite Shapes A Composite shape is a shape that is made up of 2 or more polygons. We can use what we already know about perimeter and area to calculate the total perimeter and area of composite shapes.

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Ex1. What is the perimeter and area of the following composite shape?

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Calculate the perimeter first…. *Remember, perimeter is the total length AROUND THE OUTSIDE of a shape. P = 8 + 4.5 + 3 + 3 + 4.5 = 23 cm

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Now calculate the area…. The area will be a little trickier to calculate. To help, visualize what shapes make up the composite shape. Triangle Rectangle

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Now, calculate the area of each shape separately What is the length of the base of the triangle? We can see from the composite solid that the base of the triangle is the same length as the longest side of the rectangle, 8 cm

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Area A triangle = bh = x 8 cm x 5 cm = 8 x 5 2 =20 cm 2 A rectangle = l x w = 8 x 4.5 cm = 36 cm 2 The TOTAL area will be these two areas added together: 20 cm 2 + 36 cm 2 = 56 cm 2

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