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Understanding Area Calculation of Complex Figures with Smaller Shapes

This guide explores how to divide complex figures into smaller rectangles and squares to find their total area. By breaking down figures into simpler components, we can calculate each area individually and sum them up for the total area. Examples include areas of figures measured in cm², ft², in², m², and yd². We demonstrate the calculations, such as dividing 20 cm² and 45 cm², and adding these to find a total area of 65 cm². This method applies universally across various measurement units, reinforcing the relationship between geometry and area.

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Understanding Area Calculation of Complex Figures with Smaller Shapes

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  1. Divide the figure in to 2 smaller rectangles. Find the area of each of the smaller rectangles. Add the areas of each of the smaller rectangles. Area of Complex Figures 20 cm² + 45 cm² = 65 cm² A = 20 cm² A = 45 cm² A = 45 cm²

  2. Divide the figure in to 1 rectangle and 1 square. Find the area of each of the smaller rectangles. Add the areas of each of the smaller rectangles. Area of Complex Figures 44 cm² + 25 cm² = 69 cm² A = 44 cm² A =25 cm² A = 69 cm²

  3. Divide the figure in to smaller squares and/ or rectangles. Find the area of each square and/or rectangle. Add the areas of each square and/or rectangle. Area of Complex Figures 9 ft² 9 ft² + + 24 ft² = 42 ft² 3 ft 3 ft × 3 ft 3 ft = 9 ft² 8 ft 8 ft × 3ft 3 ft × 3ft 3 ft = 24 ft² = 9 ft² A = 42 ft²

  4. Divide the figure in to smaller squares and/ or rectangles. Find the area of each square and/or rectangle. Add the areas of each square and/or rectangle. Area of Complex Figures 4 yd² + 40 yd² = 44 yd² 2 yd 2 yd × 2 yd 2 yd = 4 yd² 2 yd 6 yd × 15 yd 4 yd = 40 yd² 10 yd A = 44 yd²

  5. Divide the figure in to smaller squares and/ or rectangles. Find the area of each square and/or rectangle. Add the areas of each square and/or rectangle. Area of Complex Figures 18 in² 18 in² + + 27 in² = 63 in² 3 in 3 in 3 in × 6 in 3 in × 6 in 6 in = 18 in² = 18 in² 9 in 9 in × 3 in ? 3 in = 27 in² 9 in A = 63 in²

  6. Divide the figure in to smaller squares and/ or rectangles. Find the area of each square and/or rectangle. Add the areas of each square and/or rectangle. Area of Complex Figures 16 m² 44 m² + + 9 m² = 69 in² 11 m 3 m × 3 m 3 m 4 m × 4 m = 9 m² 4 m = 16 m² 4 m × 11 m = 44 m² 3 m 4 m 11 in ? 8 m 7 m A = 69 m² 4 m

  7. Divide the figure in to smaller squares and/ or rectangles. Find the area of each square and/or rectangle. Add the areas of each square and/or rectangle. Area of Complex Figures 24 ft² 28 ft² + + 15 ft² = 67 ft² 8 ft A = 67 ft² 3 ft × 8 ft 3 ft = 24 ft² 7 ft 4 ft 4 ft × 7 ft = 28 ft² 7 ft 5 ft 5 ft × 3 ft 3 ft ? 4 ft = 15 ft² 9 ft

  8. Your Turn! Find the area of the these complex figures by dividing them into smaller squares and/or rectangles. 5 m² + 6 m² = 11 m² 5 m 5 m × 1 m 1 m = 5 m² 1 m 6 m × 1 m 1 m = 6 m² 6 m A = 11 m²

  9. Your Turn! Find the area of the these complex figures by dividing them into smaller squares and/or rectangles. 3 in 9 in² 9 in² + + 9 in² = 27 in² 3 in × 3 in 3 in = 9 in² A = 27 in² 3 in 3 in × 3 in 3 in × 3 in 3 in = 9 in² = 9 in²

  10. Your Turn! Find the area of the these complex figures by dividing them into smaller squares and/or rectangles. 6 ft 6 ft × 3 ft 3 ft = 18 ft² 3 ft 3 ft × 2 ft 18 ft² 6 ft² + + 18 ft² = 42 ft² 2 ft = 6 ft² A = 42 ft² 6 ft × 3 ft = 18 ft²

  11. Your Turn! Find the area of the these complex figures by dividing them into smaller squares and/or rectangles. 16 cm² + 100 cm² = 116 cm² 10 cm A = 116 cm² 10 cm × 10 cm 10 cm = 100 cm² 4 cm 4 cm × 4 cm 4 cm = 16 cm²

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