1. 8-5 Area of Composite Figures Learn to break a polygon into simpler parts to find its area.

2. 8-5 Area of Composite Figures 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. 1.7 cm 4.9 cm 1.3 cm 2.1 cm

3. 8-5 Area of Composite Figures Additional Example 1A Continued A = lw A = 4.9 1.7 A = 2.1 1.3 Write the formula for the area of a rectangle. A = 8.33 A = 2.73 8.33 + 2.73 = 11.06Add to find the total area. The area of the polygon is 11.06 cm 2. 1.7 cm 4.9 cm 1.3 cm 2.1 cm

4. 8-5 Area of Composite Figures Think: Break the figure apart into a rectangle and a triangle. Find the area of each polygon. Additional Example 1B: Finding Areas of Composite Figures Find the area of the polygon.

5. 8-5 Area of Composite Figures Additional Example 1B Continued A = lw A = 28 24 A = 672 A = 168 672 + 168 = 840 Add to find the total area of the polygon. The area of the polygon is 840 ft 2. A = bh 1 2 __ A = 28 12 1 2 __

6. 8-5 Area of Composite Figures Check It Out: Example 1A Find the area of the polygon. Think: Break the polygon apart into rectangles. Find the area of each rectangle. 1.9 cm 1.5 cm 2 cm 3.4 cm 5.5 cm 1.9 cm 5.5 cm 1.5 cm 2 cm

7. 8-5 Area of Composite Figures A = lw A = 5.5 1.9 A = 2 1.5 Write the formula for the area of a rectangle. A = 10.45 A = 3 10.45 + 3 = 13.45Add to find the total area. The area of the polygon is 13.45 cm 2. Check It Out: Example 1A Continued 1.9 cm 5.5 cm 1.5 cm 2 cm

8. 8-5 Area of Composite Figures Check It Out: Example 1B Find the area of the polygon. Think: Break the figure apart into a rectangle and a triangle. Find the area of each polygon. 36 ft 22 ft 20 ft 22 ft 16 ft

9. 8-5 Area of Composite Figures A = lw A = 22 20 A = 440 A = 176 440 + 176 = 616 Add to find the total area of the polygon. The area of the polygon is 616 ft 2. A = bh 1 2 __ A = 22 16 1 2 __ Check It Out: Example 1B Continued 20 ft 22 ft 16 ft

10. 8-5 Area of Composite Figures 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 l = 5, w = 5; A = 5 5 = 25 Rectangle 2 l = 10, w = 5; A = 10 5 = 50 Rectangle 3 l = 15, w = 5; A = 15 5 = 75 Rectangle 4 l = 20, w = 5; A = 20 5 = 100 0 10 15 20 5 10 5 15 2025

11. 8-5 Area of Composite Figures Additional Example 2 Continued 25 + 50 + 75 + 100 = 250 square units. Add the areas of the four rectangles to find the total area of the design. The area of the design is 250 square units.

12. 8-5 Area of Composite Figures You can also count the squares and multiply by the area of one square. 1 square = 25 square units. 10 25 = 250 square units. Helpful Hint

13. 8-5 Area of Composite Figures 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. Rectangle 1 l = 5, w = 10; A = 5 10 = 50 Rectangle 2 l = 5, w = 15; A = 5 15 = 75 Rectangle 3 l = 5, w = 10; A = 5 10 = 50 0 10 15 20 5 10 5 15 2025 3 2 1

14. 8-5 Area of Composite Figures Check It Out: Example 2 Continued 50 + 75 + 50 = 175 square units. Add the areas of the three rectangles to find the total area of the design. The area of the design is 175 square units.