Break into Simpler Parts 10-3 Break into Simpler Parts Course 1 Warm Up Problem of the Day Lesson Presentation

Break into Simpler Parts Course 1 10-3 Break into Simpler Parts 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? 40 cm2 216 ft2 64 cm2

Break into Simpler Parts Course 1 10-3 Break into Simpler Parts 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.

Break into Simpler Parts Course 1 10-3 Break into Simpler Parts Learn to break a polygon into simpler parts to find its area.

Additional Example 1A: Finding Areas of Composite Figures Course 1 10-3 Break into Simpler Parts Additional Example 1A: Finding Areas of Composite Figures Find the area of the polygon. A. 1.7 cm 4.9 cm 1.3 cm 2.1 cm Think: Break the polygon apart into rectangles. Find the area of each rectangle.

Additional Example 1A Continued Course 1 10-3 Break into Simpler Parts Additional Example 1A Continued 1.7 cm 4.9 cm 1.3 cm 2.1 cm 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.

Additional Example 1B Continued Course 1 10-3 Break into Simpler Parts Additional Example 1B Continued Find the area of the polygon. B. Think: Break the figure apart into a rectangle and a triangle. Find the area of each polygon.

Additional Example 1B Continued Course 1 10-3 Break into Simpler Parts Additional Example 1B Continued A = bh 1 2 __ A = lw A = • 28 • 12 1 2 __ A = 28 • 24 A = 672 A = 168 Add to find the total area of the polygon. 672 + 168 = 840 The area of the polygon is 840 ft2.

Break into Simpler Parts Course 1 10-3 Break into Simpler Parts Try This: Example 1A Find the area of the polygon. A. 1.9 cm 1.9 cm 5.5 cm 5.5 cm 1.5 cm 1.5 cm 2 cm 2 cm 3.4 cm Think: Break the polygon apart into rectangles. Find the area of each rectangle.

Try This: Example 1A Continued Course 1 10-3 Break into Simpler Parts Try This: Example 1A Continued 1.9 cm 5.5 cm 1.5 cm 2 cm 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.

Break into Simpler Parts Course 1 10-3 Break into Simpler Parts Try This: Example 1B Find the area of the polygon. B. 20 ft 22 ft 16 ft 36 ft 20 ft 22 ft Think: Break the figure apart into a rectangle and a triangle. Find the area of each polygon.

Try This: Example 1B Continued Course 1 10-3 Break into Simpler Parts Try This: Example 1B Continued 16 ft 20 ft 22 ft 22 ft A = bh 1 2 __ A = lw A = • 22 • 16 1 2 __ A = 22 • 20 A = 440 A = 176 Add to find the total area of the polygon. 440 + 176 = 616 The area of the polygon is 616 ft2.

Additional Example 2: Art Application Course 1 10-3 Break into Simpler Parts Additional Example 2: Art Application Patrick made a design. All the sides are 5 inches long, except for two longer sides that are each 20 inches. All the angles are right angles. What is the area of the quilt design? 20 in. Think: Divide the design into 3 rectangles. Find the area of one rectangle that has a length of 20 in and a width of 5 in. 5 in. 20 in. A = lw Write the formula. A = 20 • 5 = 100 Multiply to find the area of the 3 rectangles. 3 • 100 = 300 The area of the design is 300 in2.

Break into Simpler Parts Course 1 10-3 Break into Simpler Parts You can also use the formula A = s2 , where s is the length of a side, to find the area of a square. Helpful Hint

Break into Simpler Parts Course 1 10-3 Break into Simpler Parts Try This: Example 2 Yvonne made quilt design. All the sides are 4 inches long, except for the two longer sides that are each 16 inches. All the angles are right angles. What is the area of the quilt design? Think: Divide the quilt design into 10 squares. Find the area of one square that has a side length of 4 in. 16 in. 4 in. 16 in. A = lw Write the formula. A = 4 • 4 = 16 Multiply to find the area of the 10 squares. 10 • 16 = 160 The area of the quilt design is 160 in2.

Break into Simpler Parts Insert Lesson Title Here Course 1 10-3 Break into Simpler Parts Insert Lesson Title Here Lesson Quiz Find the area of the figure shown. 220 units2