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Area: Triangles and Trapezoids Lesson 10-2 p.509 1. Start the Bellwork Quiz. 2. Have your HW, red pen, and book on your desk.

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Triangles When finding the area of triangles, remember that a triangle is half of a parallelogram.

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Triangles Now you can see why the formula for the area of a triangle makes sense: A = bhor A = bh 2

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Triangles Let’s look at an example: 4 feet 5 feet A = bh = 4 (5) = 20 2 2 2 or 10 ft 2

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Try This Find the areas: 12 in. 3 ft. 5 mi. 6 miles 7 miles

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Try This Find the areas: 12 in. 3 ft. 5 mi. 6 miles 7 miles 216 in 2 or 1.5 ft 2

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Try This Find the areas: 12 in. 3 ft. 5 mi. 6 miles 7 miles 216 in 2 or 1.5 ft 2 15 mi 2

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Trapezoids Trapezoids have different formula. It looks like this: A = h (b 1 + b 2 ) or A = h(b 1 + b 2 ) 2 b1b1 b2b2 h

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Trapezoids A = h (b 1 + b 2 ) or A = h(b 1 + b 2 ) 2 Note that there are 2 bases—base 1 and base 2. The formula takes the average of the two bases multiplied by the height. b1b1 b2b2 h

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Trapezoids Let’s try an example: A = h (b 1 + b 2 ) A = 3.5 (4 + 6) 2 2 A = 3.5 (5) = 17.5 ft 2 4 ft 6 feet 3.5 ft

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Try This Find the area: 24 mm 33 mm 12 mm

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Try This Find the area: 24 mm 33 mm 12 mm 342 mm 2

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Try This Find the area: 4 feet 2 feet 4.5 feet

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Try This Find the area: 4 feet 2 feet 4.5 feet 13 ft 2

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Example Some shapes look unusual, but when you remember just 3 formulas, you can calculate the area. Which two shapes do you see in the figure at the left?

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Example There is a square (parallelogram) and a triangle. To find the area, first find the area of the parallelogram and then add it to the area of the triangle.

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Example 3 ft 2 ft The square has an area of A = bh or 3 (3) or 9 ft 2. The triangle has an area of A = ½ bh or ½ (3) (2) or 3 ft 2. The total area if 9 + 3 or 12 ft 2

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Try This Find the area: 4 cm 6 cm 8 cm 6 cm

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Try This Here is a hint: 4 cm 6 cm 8 cm 6 cm

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Try This Here is a hint: 4 cm 6 cm 8 cm 6 cm For the rectangle: A = bh A = 6 (4) = 24 cm 2 For the trapezoid: A = ½ h (b 1 + b 2 ) A = ½ (2) (4 + 6) A = 10 cm 2 Total area = 24 + 10 = 34 cm 2

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Try This Is there another way to divide this up? 4 cm 6 cm 8 cm 6 cm

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Try This How about like this: 4 cm 6 cm 8 cm 6 cm

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Try This How about like this: 4 cm 6 cm 8 cm 6 cm For the rectangle: A = bh = 8 (4) = 32 cm 2 For the triangle: A = ½ bh = ½ (2) (2) = 2 cm 2 The total area is 32 + 2 or 34 cm 2

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Agenda PA#38 Pp.512-513 #8-16 even, 17, 19

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Please start Bellwork # HW, red pen book on desk.

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Agenda PA# Workbook pp.83 & 84 Benchmark 3 is Friday.

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