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**7.3 Area of Complex Figures**

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**7.3 Area of Complex Figures**

What are the formulas for the areas of a parallelogram, triangle, trapezoid, and circle? What is the circumference formula for a circle? Parallelogram A = bh Triangle A = ½ bh Circle C = Πd or 2Πr Trapezoid A = ½ h(b1 + b2) Circle A = Πr2

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**Example 1 4 Triangle A = ½ bh A = ½ (12)(4) A = 24 Rectangle A = bh**

Find the area of the complex figure. How can this figure be separated? What are the formulas that are needed to solve this problem? The area of the figure is This equals 204. 4 Triangle A = ½ bh A = ½ (12)(4) A = 24 Rectangle A = bh A = 12(15) A = 180 12 15 NOW WHAT!?!

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**Semi-circle A = ½ Πr2 Triangle A = ½ bh A = ½ (6)(11) A = 33 Example 2**

Find the area of the complex figure. What formulas do we use? Semi-circle A = ½ Πr2 A = ½ Π (3)2 A = 14.1 6 Triangle A = ½ bh A = ½ (6)(11) A = 33 11 Now what!?! Add the areas together. = 37.1

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**Example 3 6 6 16 8 24 Triangle A = ½ bh A = ½ (12)(8) A = 48 Rectangle**

Find the area of the complex figure. What shapes can this be separated into? What are the formulas needed? Triangle A = ½ bh A = ½ (12)(8) A = 48 6 6 16 Rectangle A = bh A = 8(24) A = 192 8 24 Add the areas together = 240

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**Practice 10 Circle A = Πr2 A = Π(3.5)2 A = 38.5 7 Rectangle A = bh**

Find the area of the complex figures. 10 2 half circles = 1 whole circle Circle A = Πr2 A = Π(3.5)2 A = 38.5 7 Rectangle A = bh A = 7(10) A = 70 = 108.5

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**Practice… 8 5 6 6 6 6 6 Add them up! 36 + 36 + 65 = 137 Square A = s2**

Remember: there are 2 squares Trapezoid A = ½ h(b1 +b2) A = ½ 5 (18 + 8) A = ½ 5(26) A = 65 8 5 6 6 6 6 6 Add them up! = 137

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