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10-3

Area of Composite Figures. 10-3. Course 1. Warm Up. Problem of the Day. Lesson Presentation. 40 cm 2. 216 ft 2. 64 cm 2. Warm Up 1. What is the area of a rectangle with length 10 cm and width 4 cm? 2. What is the area of a parallelogram with base 18 ft and height 12 ft?

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10-3

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  1. Area of Composite Figures 10-3 Course 1 Warm Up Problem of the Day Lesson Presentation

  2. 40 cm2 216 ft2 64 cm2 Warm Up 1.What is the area of a rectangle with length 10 cm and width 4 cm? 2. What is the area of a parallelogram with base 18 ft and height 12 ft? 3. What is the area of a triangle with base 16 cm and height 8 cm?

  3. Problem of the Day Four squares are stacked in a tower. The bottom square is 12 inches on a side. The perimeter of each of the other squares is half of the one below it. What is the perimeter of the combined figure? 69 in.

  4. Learn to break a polygon into simpler parts to find its area.

  5. 1.7 cm 1.3 cm 4.9 cm 2.1 cm Additional Example 1A: Finding Areas of Composite Figures Find the area of the polygon. Think: Break the polygon apart into rectangles. Find the area of each rectangle.

  6. 1.7 cm 1.3 cm 4.9 cm 2.1 cm Additional Example 1A Continued A =lw A =lw Write the formula for the area of a rectangle. A = 4.9•1.7 A = 2.1 •1.3 A = 8.33 A = 2.73 8.33 + 2.73 = 11.06 Add to find the total area. The area of the polygon is 11.06 cm2.

  7. Additional Example 1B: Finding Areas of Composite Figures Find the area of the polygon. Think: Break the figure apart into a rectangle and a triangle. Find the area of each polygon.

  8. A =bh A = •28 •12 1 1 __ __ 2 2 Additional Example 1B Continued A =lw A = 28•24 A = 168 A = 672 Add to find the total area of the polygon. 672 + 168 = 840 The area of the polygon is 840 ft2.

  9. 1.9 cm 1.5 cm 5.5 cm 2 cm Check It Out: Example 1A Find the area of the polygon. 1.9 cm 5.5 cm 1.5 cm 2 cm 3.4 cm Think: Break the polygon apart into rectangles. Find the area of each rectangle.

  10. 1.9 cm 1.5 cm 5.5 cm 2 cm Check It Out: Example 1A Continued A =lw A =lw Write the formula for the area of a rectangle. A = 5.5•1.9 A = 2 •1.5 A = 10.45 A = 3 10.45 + 3 = 13.45 Add to find the total area. The area of the polygon is 13.45 cm2.

  11. 16 ft 22 ft 20 ft 22 ft Check It Out: Example 1B Find the area of the polygon. 36 ft 20 ft 22 ft Think: Break the figure apart into a rectangle and a triangle. Find the area of each polygon.

  12. A =bh A = •22 •16 1 1 __ __ 2 2 Check It Out: Example 1B Continued 16 ft 20 ft 22 ft 22 ft A =lw A = 22•20 A = 176 A = 440 Add to find the total area of the polygon. 440 + 176 = 616 The area of the polygon is 616 ft2.

  13. Additional Example 2: Art Application Patrick made a design. Use the coordinate grid to find its area. Think: Divide the design into rectangles. Find the area of each rectangle. Rectangle 1 25 l = 5, w = 5; A = 5 • 5 = 25 20 Rectangle 2 15 l = 10, w = 5; A = 10 • 5 = 50 10 Rectangle 3 5 l = 15, w = 5; A = 15 • 5 = 75 0 10 5 15 20 25 Rectangle 4 l = 20, w = 5; A = 20 • 5 = 100

  14. Additional Example 2 Continued Add the areas of the four rectangles to find the total area of the design. 25 + 50 + 75 + 100 = 250 square units. The area of the design is 250 square units.

  15. Helpful Hint You can also count the squares and multiply by the area of one square. 1 square = 25 square units. 10 • 25 = 250 square units.

  16. Check It Out: Example 2 Lawanda made a design. Use the coordinate grid to find its area. Think: Divide the design into rectangles. Find the area of each rectangle. 25 Rectangle 1 20 l = 5, w = 10; A = 5 • 10 = 50 1 15 2 Rectangle 2 10 3 l = 5, w = 15; A = 5 • 15 = 75 5 0 10 5 15 20 25 Rectangle 3 l = 5, w = 10; A = 5 • 10 = 50

  17. Check It Out: Example 2 Continued Add the areas of the three rectangles to find the total area of the design. 50 + 75 + 50 = 175 square units. The area of the design is 175 square units.

  18. Lesson Quiz 1. Find the area of the figure shown. 220 units2 2. Phillip designed a countertop. Use the coordinate grid to find its area. 30 units2

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