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Area of Rectangles, Parallelograms, Triangles, and Composite Figures

Learn how to find the area of different shapes such as rectangles, parallelograms, triangles, and composite figures. Practice solving problems and take quizzes to test your knowledge.

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Area of Rectangles, Parallelograms, Triangles, and Composite Figures

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  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 placed in a row. The square on the far left is 12 inches on a side. The perimeter of each of the other squares is half of the one to its left. 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. 1 __ A =bh 2 1 __ A = •28 •12 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. 1 __ A =bh 2 1 __ A = •22 •16 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 Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  19. 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

  20. Lesson Quiz for Student Response Systems 1. Find the area of the figure. A. 27 units2B. 54 units2 C. 93 units2D. 98 units2

  21. Lesson Quiz for Student Response Systems 2. Paul arranged tiles to form a model. Use the coordinate grid to identify its area. A. 25 square units B. 18 square units C. 21 square units D. 16 square units

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