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## Measurement

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**Area of Square**• Square A = l x w A = 4 x 4 W = 4 A = 16 units2 L = 4**Area of Rectangle**• Rectangle A = l x w A = 6 x 4 W = 4 A = 24 units2 L = 6**Area of a Triangle**• Triangle A = ½ (b x h) A = ½ (4 x 4) h = 4 A = ½ (16) A = 8 units2 b = 4**Finding the Area of Regular Shapes**• Square A = l x w • Rectangle A = l x w • Triangle A = ½ (b x h)**Break the shape apart into shapes you know how to find the**area of….**Becomes……….**+ +**Becomes……….**+ +**We can use this strategy to help us find the area of a**parallelogram by changing the location of the end triangles + + + =**Therefore the area of a parallelogram is….. A = b x h**h = 3 b = 5**Can we apply the same strategies to finding the area of a**trapezoid……? b1 Where b1 and b2 represent the parallel sides h is the height h b2**Using graph paper, draw a trapezoid with the following**units… Now, see if you can break it apart into different shapes, rearrange and find a new formula…… b1 = 3 h= 4 b2 = 5**Copy, Reflect, and Translate the trapezoid……what shape**do you have now???? Do you know the formula for this new shape? How can you modify it for a TRAPEZOID? b1 = 3 h= 4 b2 = 5**Now we have a parallelogram….**only it’s 2x’s as big as the trapezoid b1 = 3 h= 4 h= 4 b2 = 5 b2 = 5**b2 = 5**b1 = 3 h= 4 b2 = 5 b1 = 3 The are of this PARALLELOGRAM is A = base x height A = (b1 + b2) x height**b2 = 5**b1 = 3 h= 4 b2 = 5 b1 = 3 It doesn’t matter which type of trapezoid you use, copy, rotate and put the 2 together and you get a parrallelogram!!!! A = ½ [ (b1 + b2) x h ]**b2 = 7**b1 = 3 h= 4 b2 = 7 b1 = 3 But, because the TRAPEZOID is only half the size of the parallelogram, we need to take half of the area….. A = (b1 + b2) x h 2**b2 = 6**b1 = 3 h= 4 b2 = 6 b1 = 3 But, because the TRAPEZOID is only half the size of the parallelogram, we need to take half of the area….. A = (b1 + b2) x h 2**A = ½ [ (b1 + b2) x h ]**Or A = [ (b1 + b2) x h ] / 2 Or A = (b1 + b2) x h 2**Is there another way????**b1 = 4 cm 3 cm b2 = 7 cm**We can divide the trapezoid into 2 Triangles**b1 = 4 cm 3 cm 3 cm b2 = 7 cm**b1 = 4 cm**3 cm b2 = 7 cm 3 cm You should notice that the height should be the same for both triangles.**b1 = 4 cm**3 cm b2 = 7 cm 3 cm Area = Triangle 1 + Triangle 2 A = b1 x h + b2 x h2 2**b1 = 6**h= 8 b2 = 10 Find the area of the following Trapezoids. b1 = 2 h= 6 b2 = 8