1. Bell Work: Simplify -(-4) + (-2) + (-(-6)) -(+4) – (-5) + 5 – (-3) + (-6)

2. Answer: -4 3

3. Lesson 8: Area

4. Area*: The number that tells how many square units are contained in a closed figure.

5. Square Unit*: A square having sides that measure one unit in length.

6. For many closed figures with irregular boundaries, we must “break up” some of the square units to fill the figure. Therefore it is not uncommon to have closed figures whose areas contain fractional square units.

7. Counting square units is not the easiest or the best way to find the area of a closed figure so we will be discussing some formulas to make computing areas easier.

8. Areas of Rectangles and Squares: This rectangle is 4 units by 9 units. We see that it takes 36 squares to fill the rectangle or 36 square units.

9. From this we find that the area of a rectangle equals the length times the width. Area of rectangle = length x width

10. A square is a rectangle so the area formula for a rectangle also applies. Since all sides are the same then the formula is, Area of a square = (length of a side) 2

11. Example: Find the area of this figure.

12. Answer: (3 x 3) + (2 x 9) 9 + 18 = 27 inches 2

13. Example: Find the area of the shaded portion of this figure.

14. Answer: (30 x 15) – (9 x 22) 450 – 198 = 252 cm 2

15. Areas of triangles: The altitude or height of a triangle is the perpendicular distance from either the base of the triangle or an extension of the base.

16. The height can be one of the sides of the triangle, fall inside the triangle or fall outside the triangle. When it falls outside the triangle, we have to extend the base so that the height can be drawn.

18. Area of a triangle = base x height 2 Find the area.

19. Answer: = 5.2 x 4.2 2 = 10.92 units 2

20. Example: Find the area of this figure.

21. Answer: = (12)(12) + (8)(12) 2 = 144 + 48 = 192 units 2

22. Area of Circles: Area of a circle = π r r = radius 2

23. Example: The radius of a circle is 3cm. Find the area of the circle.

24. Answer: Area = (3.14)(3cm) = (3.14)(9cm ) = 28.26cm 2 2 2

25. Example: Find the area of this figure.

26. Answer: = (2)(3) + (5)(7) + (3.14)(2) 2 = 3 + 35 + 6.28 = 44.28cm 2 2

27. Area of a parallelogram or trapezoid: Area = A + A In other words, separate the parallelogram or trapezoid into two triangles and add the area of each triangle together. 12

28. Example: Find the area of the parallelogram.

29. Answer: = (4)(2) + (4)(2)2 = 4 + 4 = 8m 2

30. HW: Lesson 8 #1-30 Due Tomorrow