1. 1/28/201610-3: Area of Polygons1 10-3: Area of Parallelograms G1.4.1: Solve multistep problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids. G1.4.3: Describe and justify hierarchical relationships among quadrilaterals (e.g., every rectangle is a parallelogram). G1.5.1: Know and use subdivision or circumscription methods to find areas of polygons (e.g., regular octagon, nonregular pentagon). G1.4.1: Solve multistep problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids. G1.4.3: Describe and justify hierarchical relationships among quadrilaterals (e.g., every rectangle is a parallelogram). G1.5.1: Know and use subdivision or circumscription methods to find areas of polygons (e.g., regular octagon, nonregular pentagon).

2. Daily Quiz 5/19 Betty is 4 feet tall and has to look up at an angle of 23° to see the top of a tree. If she is 25 feet away from the tree, how tall is the tree (to the nearest foot)?

3. 1/28/201610-3: Area of Polygons3 Area Area is the number of non-overlapping squares inside a 2 dimensional shape. Area is always measured in ________ units, such as ___, ____ or _____. Remember the word “square” is always said before the units. Area is the number of non-overlapping squares inside a 2 dimensional shape. Area is always measured in ________ units, such as ___, ____ or _____. Remember the word “square” is always said before the units.

4. 1/28/201610-3: Area of Polygons4 Area of a Rectangle Postulate If a rectangle has length of L units, width of W units and area of A square units, then A = _____.

5. 1/28/201610-3: Area of Polygons5 Area of a Rectangle 8 units 6 units

6. 1/28/201610-3: Area of Polygons6 Parallelograms

7. 1/28/201610-3: Area of Polygons7 Anatomy of a Parallelogram Any side of a parallelogram can be the base. The altitude of a parallelogram is a segment with its endpoints on the lines containing the bases, perpendicular to the bases. The height of the parallelogram is the length of the altitude.

8. 1/28/201610-3: Area of Polygons8 base 1 base 2 altitude

9. 1/28/201610-3: Area of Polygons9 base 1 base 2 altitude

10. 1/28/201610-3: Area of Polygons10 What is the area of the parallelogram below and why? 13 feet 6 feet

11. 1/28/201610-3: Area of Polygons11 Area of a Parallelogram Formula If the base of a parallelogram is b units,the height is h units and the area is A square units, then A = ______. If the base of a parallelogram is b units,the height is h units and the area is A square units, then A = ______.

12. 1/28/201610-3: Area of Polygons12 Calculate the area of the parallelogram below. Remember the proper units. 10 mm 8 mm 21 mm

13. 1/28/201610-3: Area of Polygons13 What is the area of a parallelogram with vertices at (0,0), (2,3), (5,0) and (7,3)? A. 10 B. 14 C. 15 D. 21 E. 35

14. 1/28/201610-3: Area of Polygons14 Determine the area of the figure below 2 different ways. Assume all angles are right angles. 3 cm 4 cm 8 cm 4 cm

16. 1/28/201610-3: Area of Polygons16 Use this slide to make your second calculation. 3 cm 4 cm 8 cm 4 cm

18. Parallelogram ABCD, with dimensions in inches, is shown in the diagram below. What is the area of the parallelogram, in square inches? A. 60 B. 72 C. 180 D. 240 E. 260 Parallelogram ABCD, with dimensions in inches, is shown in the diagram below. What is the area of the parallelogram, in square inches? A. 60 B. 72 C. 180 D. 240 E. 260 1/28/201610-3: Area of Polygons18 13 5 15 D C B A

19. 1/28/201610-3: Area of Polygons19 Calculate the area of the shaded region below. The angles that appear to be right angles are right angles. 24 in 34 in 8 in

20. 1/28/201610-3: Area of Polygons20 Calculate the area of the shaded (red) region below. The angles that appear to be right angles are right angles. 5 in 6 in 2 in 3 in 2 in 9.5 in 1 in 4 in

21. 1/28/201610-3: Area of Polygons21 A floor has the dimensions shown below. How many square feet of tile are needed to cover the entire floor? A. 50 B. 95 C. 160 D. 190 E. 220 A floor has the dimensions shown below. How many square feet of tile are needed to cover the entire floor? A. 50 B. 95 C. 160 D. 190 E. 220 19 feet 10 feet 5 feet 16 feet

22. 1/28/201610-3: Area of Polygons22 In the parallelogram below, lengths are given in inches. What is the area of the parallelogram, in square inches? A.√94 B.7 √47 C. 49 D. 63 E. 16 √47 In the parallelogram below, lengths are given in inches. What is the area of the parallelogram, in square inches? A.√94 B.7 √47 C. 49 D. 63 E. 16 √47 7 √479

23. 1/28/201610-3: Area of Polygons23 Identify the quadrilateral with given vertices as a parallelogram, rectangle or square and then determine its area. A(-4, -5), B(2, -5), C(4, -8), D(-2, -8)

24. 1/28/201610-3: Area of Polygons24 The measures of the angles of a triangle are in the ratio of 2x:3x:5x as illustrated below. What is the measure of the smallest angle? A. 18 B. 20 C. 30 D. 36 E. 40 The measures of the angles of a triangle are in the ratio of 2x:3x:5x as illustrated below. What is the measure of the smallest angle? A. 18 B. 20 C. 30 D. 36 E. 40 2x° 5x° 3x°

25. 1/28/201610-3: Area of Polygons25 Assignment 10-3.1 Pages 532 - 533, # 11 - 19 (odds) Pages 532 - 533, # 11 - 19 (odds)

26. 1/28/201610-3: Area of Polygons26 Assignment 10-3.2 Pages 532 - 533, # 10 - 20 (evens) Pages 532 - 533, # 10 - 20 (evens)