area: triangles and trapezoids lesson 10-2 p.509 1. start the bellwork quiz. 2. have your hw, red...
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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 = bh or A = bh 2
12
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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 ft2
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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 in2 or1.5 ft2
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Try This Find the areas:
12 in.
3 ft.5 mi.
6 miles
7 miles
216 in2 or1.5 ft2 15 mi2
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Trapezoids Trapezoids have different formula. It looks
like this:
A = h (b1 + b2) or A = h(b1 + b2)
2b1
b2
h
12
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Trapezoids A = h (b1 + b2) or A = h(b1 + b2)
2Note that there are 2 bases—base 1 and
base 2. The formula takes the average of the two bases multiplied by the height.
b1
b2
h
12
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Trapezoids Let’s try an example:
A = h (b1 + b2) A = 3.5 (4 + 6)
2 2A = 3.5 (5) = 17.5 ft2
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 mm2
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Try This Find the area:
4 feet2 feet
4.5 feet
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Try This Find the area:
4 feet2 feet
4.5 feet13 ft2
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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 yousee 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 ft2.The triangle has an area of A = ½ bh or ½ (3) (2) or 3 ft2.The total area if 9 + 3 or 12 ft2
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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 = bhA = 6 (4) = 24 cm2
For the trapezoid:A = ½ h (b1 + b2)A = ½ (2) (4 + 6)A = 10 cm2
Total area =24 + 10 = 34 cm2
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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 cm2
For the triangle:A = ½ bh = ½ (2) (2) = 2 cm2
The total area is 32 + 2 or34 cm2
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Agenda
PA#38Pp.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.