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Geometry Composite Figures

Geometry Composite Figures. Warm up. Find the area of each regular polygon. Round to the nearest tenth: 1) An equilateral triangle with a side length of 3 cm. 2) A regular hexagon with an apothem of 4√3 m. Composite Figures.

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Geometry Composite Figures

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  1. Geometry Composite Figures CONFIDENTIAL

  2. Warm up Find the area of each regular polygon. Round to the nearest tenth: 1) An equilateral triangle with a side length of 3 cm. 2) A regular hexagon with an apothem of 4√3 m. CONFIDENTIAL

  3. Composite Figures A composite figure is made up of simple shapes such as triangles, rectangles, trapezoids and circles. To find the area of a composite figure, find the areas of the simple shapes and then use the Area Addition Postulate. CONFIDENTIAL

  4. Finding the area of Composite Figures by Adding A) Find the area of the shaded region. 15 cm 12 cm Divide the figure into rectangles. Area of top rectangle: A = bh = 12(15) = 180 cm2 Area of bottom rectangle: A = bh = 9(27) = 243 cm2 Shaded area: 180 cm2 + 243 cm2 = 423 cm2 21 cm 27 cm 15 cm 12 cm 12 cm 9 cm 27 cm CONFIDENTIAL

  5. Finding the area of Composite Figures by Adding B) Divide the figure into parts. The base of the triangle is : √(10.22 - 4.82) = 9 ft Area of triangle: A = 1bh = 1(9)(4.8) = 21.6 ft2 2 2 Area of rectangle: A = bh = 9(3) = 27 ft2 Area of half circle: A = 1∏r2 = 1∏(4.52) = 10.125∏ ft2 2 2 Shaded area: 21.6 + 27 + 10.125∏ ≈ 80.4 ft2 10.2 ft 10.2 ft 7.8 ft 7.8 ft 3 ft 3 ft 4.5 ft CONFIDENTIAL

  6. Now you try! 1) Find the area of the given figure. Round to the nearest tenth. 62.5 m 37.5 m 22.5 m 75 m CONFIDENTIAL

  7. Sometimes you need to subtract to find the area of composite figures. CONFIDENTIAL

  8. Finding the area of Composite Figures by Subtracting A) Find the area of the shaded region. 9 m Subtract the area of the triangle from the area of the rectangle. Area of top rectangle: A = bh = 18(36) = 648 m2 Area of triangle: A = 1bh = 1(36)(9) = 162 m2 2 2 Area of the figure: A = 648 – 162 = 486 m2 18 m 36 m CONFIDENTIAL

  9. B) Find the area of the shaded region. The two half circles have the same area as one circle. Subtract the area of the circle from the area of the rectangle. Area of top rectangle: A = bh = 33(16) = 528 ft2 Area of circle: A = ∏r2 = ∏(82) = 64∏ ft2 Area of the figure: A = 528 – 64∏ = 326.9 ft2 16 ft 33 ft CONFIDENTIAL

  10. Now you try! 2) Find the area of the shaded region. Round to the nearest tenth. 6 in CONFIDENTIAL

  11. Katie is using the given plan to convert part of her lawn to a xeriscape garden. A newly planted xeriscope uses 17 gallons of water per square foot per year. How much water will the garden require in one year? Divide the garden into parts. Area of top rectangle: A = bh = 28.5(7.5) = 213.75 ft2 Area of center trapezoid: A = 1(12 + 18)(6) = 90 ft2 2 Area of bottom rectangle: A = bh = 12(6) = 72 ft2 Area of the garden is: 213.75 + 90 + 72 = 375.75 ft2 28.5 ft 7.5 ft 19.5 ft 18 ft 10.5 ft 6 ft 12 ft 28.5 ft 7.5 ft 19.5 ft 18 ft 10.5 ft The garden will use (375.75)(17) = 6387.75 gallons of water per year 6 ft 12 ft CONFIDENTIAL

  12. Now you try! 3) The lawn that Katie is replacing requires 79 gallons of water per square foot per year. How much water will Katie save by planting the xeriscape garden? 28.5 ft 7.5 ft 19.5 ft 18 ft 10.5 ft 6 ft 12 ft CONFIDENTIAL

  13. To estimate the area of an irregular shape, you can sometimes use a composite figure. First draw a composite figure that resembles the irregular shape. Then divide the composite figure into simple shapes. CONFIDENTIAL

  14. Estimating areas of irregular shapes Use a composite figure to estimate the shaded area. The grid gas squares with side length of 1 cm. Draw a composite figure that approximates the irregular shape. Find the area of each part of the composite figure. Area of triangle, a: A = 1bh = 1(3)(1) = 1.5 cm2 2 2 Area of Parallelogram, b: A = bh = 3(1) = 3 cm2 a b c d CONFIDENTIAL

  15. Area of trapezoid, c: A = 1(3 + 2)(1) = 2.5 cm2 2 Area of triangle, d: A = 1bh = 1(2)(1) = 1 cm2 2 2 Area of composite figure: 1.5 + 3 + 2.5 + 1 = 8 cm2 a b c d The shaded area is about 375.75 ft2 CONFIDENTIAL

  16. Now you try! 4) Use a composite figure to estimate the shaded area. The grid gas squares with side length of 1 ft. CONFIDENTIAL

  17. Now some problems for you to practice ! CONFIDENTIAL

  18. Assessment Find the area of the shaded region. Round to the nearest tenth: 4 cm 1) 3 cm 5 cm 2 cm 12 cm 2) 4 ft 5 ft CONFIDENTIAL

  19. 18 in. 3) 3 in. 8 in. 6 m 4) 2 m 3 m 5 m CONFIDENTIAL

  20. Find the area of the shaded region. Round to the nearest tenth: 16 ft 12 cm 6) 5) 12 ft 12 ft 4 ft 12 cm 12 cm CONFIDENTIAL

  21. Shelby is planting grass in an irregularly shaped garden as shown The grid has squares of side 1 yd. Estimate the area of the garden. Given that grass cost $6.50 per square yard, find the cost of the grass. CONFIDENTIAL

  22. Let’s review Composite Figures A composite figure is made up of simple shapes such as triangles, rectangles, trapezoids and circles. To find the area of a composite figure, find the areas of the simple shapes and then use the Area Addition Postulate. CONFIDENTIAL

  23. Finding the area of Composite Figures by Adding A) Find the area of the shaded region. 15 cm 12 cm Divide the figure into rectangles. Area of top rectangle: A = bh = 12(15) = 180 cm2 Area of bottom rectangle: A = bh = 9(27) = 243 cm2 Shaded area: 180 cm2 + 243 cm2 = 423 cm2 21 cm 27 cm 15 cm 12 cm 12 cm 9 cm 27 cm CONFIDENTIAL

  24. B) Find the area of the shaded region. The two half circles have the same area as one circle. Subtract the area of the circle from the area of the rectangle. Area of top rectangle: A = bh = 33(16) = 528 ft2 Area of circle: A = ∏r2 = ∏(82) = 64∏ ft2 Area of the figure: A = 528 – 64∏ = 326.9 ft2 16 ft 33 ft CONFIDENTIAL

  25. Katie is using the given plan to convert part of her lawn to a xeriscape garden. A newly planted xeriscope uses 17 gallons of water per square foot per year. How much water will the garden require in one year? Divide the garden into parts. Area of top rectangle: A = bh = 28.5(7.5) = 213.75 ft2 Area of center trapezoid: A = 1(12 + 18)(6) = 90 ft2 2 Area of bottom rectangle: A = bh = 12(6) = 72 ft2 Area of the garden is: 213.75 + 90 + 72 = 375.75 ft2 28.5 ft 7.5 ft 19.5 ft 18 ft 10.5 ft 6 ft 12 ft 28.5 ft 7.5 ft 19.5 ft 18 ft 10.5 ft The garden will use (375.75)(17) = 6387.75 gallons of water per year 6 ft 12 ft CONFIDENTIAL

  26. Estimating areas of irregular shapes Use a composite figure to estimate the shaded area. The grid gas squares with side length of 1 cm. Draw a composite figure that approximates the irregular shape. Find the area of each part of the composite figure. Area of triangle, a: A = 1bh = 1(3)(1) = 1.5 cm2 2 2 Area of Parallelogram, b: A = bh = 3(1) = 3 cm2 a b c d CONFIDENTIAL

  27. Area of trapezoid, c: A = 1(3 + 2)(1) = 2.5 cm2 2 Area of triangle, d: A = 1bh = 1(2)(1) = 1 cm2 2 2 Area of composite figure: 1.5 + 3 + 2.5 + 1 = 8 cm2 a b c d The shaded area is about 375.75 ft2 CONFIDENTIAL

  28. You did a great job today! CONFIDENTIAL

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