1. Estimating and Finding Area Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

2. Learn to estimate the area of irregular figures and to find the area of rectangles and parallelograms. Course 1 Estimating and Finding Area TEKS 6.8.B: Measurement: select and use appropriate units, tools or formulas to measure and to solve problems…

3. Vocabulary area Insert Lesson Title Here Course 1 Estimating and Finding Area

4. The area of a figure is the amount of surface it covers. We measure area in square units. Course 1 Estimating and Finding Area

5. Course 1 Estimating and Finding Area

6. Additional Example 2: Finding the Area of a Rectangle Find the area of the figure. Write the formula. Substitute 15 for l. Substitute 9 for w. A = lw A = 15 9 A = 135 The area is about 135 in 2. 15 in. 9 in. Course 1 Estimating and Finding Area

7. You can use the formula for the area of a rectangle to write a formula for the area of a parallelogram. Imagine cutting off the triangle drawn in the parallelogram and sliding it to the right to form a rectangle. The area of a parallelogram = bh. The area of a rectangle = lw. The base of the parallelogram is the length of the rectangle. The height of the parallelogram is the width of the rectangle. Course 1 Estimating and Finding Area

8. Additional Example 3: Finding the Area of a Parallelogram Find the area of the parallelogram. Write the formula. Multiply. A = bh 2 ft 1 2 A = 2 1 1 2 __ 1 4 Substitute 2 for b and 1 for h. 1 2 __ 1 4 A = 5 2 __ 5 4 A = or 3 25 8 ___ 1 8 __ The area is 3 ft 2. 1 8 __ 1 4 1 ft Course 1 Estimating and Finding Area

9. Course 1 Estimating and Finding Area You can divide any parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram. Base Height Base Area of Triangles

10. Course 1 Estimating and Finding Area AREA OF A TRIANGLE b A = 1212 bhbh The area A of a triangle is half the product of its base b and its height h. h

11. Course 1 Estimating and Finding Area Find the area of the triangle. Additional Example 1A: Finding the Area of a Triangle A = 1212 bh Write the formula. A = 1212 (20 · 12) Substitute 20 for b and 12 for h. A = 120 The area is 120 ft 2. A = 1212 (240) Multiply.

12. Course 1 Estimating and Finding Area Find the area of the triangle. Additional Example 1B: Finding the Area of a Triangle A = 1212 bh Write the formula. A = 1212 (30 · 24) Substitute 30 for b and 24 for h. A = 360 The area is 360 in 2. A = 1212 (720) Multiply.

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14. Course 1 Estimating and Finding Area Additional Example 1A: Estimating the Area of a Circle Estimate the area of the circle. Use 3 to approximate pi. A ≈ 3 20 2 A ≈ 1200 m 2 19.7 m A = r 2 Write the formula for area. Replace  with 3 and r with 20. A ≈ 3 400 Use the order of operations. Multiply.

15. Course 1 Estimating and Finding Area Additional Example 1B: Estimating the Area of a Circle Estimate the area of the circle. Use 3 to approximate pi. r = 28 ÷ 2 A ≈ 3 14 2 28 m A = r 2 Write the formula for area. Replace  with 3 and r with 14. r = 14 Use the order of operations. Divide. r = d ÷ 2 The length of the radius is half the length of the diameter. A ≈ 3 196A ≈ 588 m 2 Multiply.

16. Course 1 Estimating and Finding Area 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

17. Course 1 Estimating and Finding Area 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

18. Course 1 Estimating and Finding Area 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.

19. Course 1 Estimating and Finding Area 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 __

20. Course 1 Estimating and Finding Area Lesson Quiz 1. Find the area of the figure shown. 220 units 2 2. Phillip designed a countertop. Use the coordinate grid to find its area. 30 units 2