1. Mrs. Williams is dividing her class into groups again! She has a class with 24 girls and 18 boys. If she wants the boys and girls distributed evenly into groups, how many groups does she need? How many boys and girls will be in each one? a)6 groups: 4 girls, 3 boys b)8 groups: 3 girls, 4 boys c)6 groups: 3 girls, 4 boys d)8 groups, 3 girls, 4 boys

2. Learn to find the perimeter and missing side lengths of a polygon. The perimeter of a figure is the distance around it. To find the perimeter you can add the lengths of the sides. Perimeter is equal to the sum of the sides

3. Perimeter of Polygons

4. Finding the Perimeter of a Polygon Find the perimeter of the figure. 2.8 3.6 3.5 3.0 + 4.3 Add all the side lengths. The perimeter is 17.2 in. P = sos

5. Find the perimeter of the figure. P = sos 3.3 4.2 + 3.0 Add all the side lengths. 3.3 in. 4.2 in. 3 in. The perimeter is 18 in.

6. P = 2( l + w) P = 2l + 2w P = l + l + w + w PLEASE tell me you recognize a property used in the top two formulas!! This formula means to find the sum of the sides P = 2(l + w)

7. Find the perimeter P of the rectangle. P = 2(l + w) Substitute 15 for l and 2 for w. P = 2(15 + 2) P = 2(17) P = 34 Multiply. Add Add. Multiply The perimeter is 34 cm. 15 cm 2 cm The top two formulas are shown….. For the two rectangles in your notes, write, substitute and solve to find the perimeters. P = 2l + 2w P = 2(15) + 2(2) P = 30+ 4 P = 34

8. Using a Formula to Find Perimeter Find the perimeter P of the rectangle. P = 2l+ 2w Substitute 12 for l and 3 for w. P = (2 12) + (2 3) P = 24 + 6 P = 30 Multiply. Add. Add. Multiply The perimeter is 30 cm. 12 cm 3 cm P = 2(l+ w) P = 2(12+ 3) P = 2(15) P = 30

9. l = 4w l = (4 9) l = 36 Finding Unknown Side Lengths and the Perimeter of a Polygon The width of a rectangle is 9 mm. What is the perimeter of the rectangle if the length is 4 times the width? length = 4w 4w4w 9 36 P = 2 l + 2 w P = 2(36) + 2 (9) P = 72 + 18 P = 90

10. What is the length of side a if the perimeter equals 61 mm? P = sum of side lengths P = SOS Use the values you know. 61 = 12 + 7 + 10 + 13 + 11 + a 61 = 53 + a – 53 = – 53 Add the known lengths. Subtract 53 from both sides. 8 = a Side a is 8 mm long. Finding Unknown Side Lengths and the Perimeter of a Polygon Find each unknown measure. 7 mm 10 mm 13 mm 11 mm 12 mm a

11. Finding Unknown Side Lengths and the Perimeter of a Polygon Find each unknown measure. B. What is the perimeter of the polygon? First find the unknown side length. Find the sides opposite side b. The length of side b = 50 + 22. Side b is 72 cm long. P = 72 + 55 + 50 + 33 + 22 + 22 P = 254 Find the perimeter. The perimeter of the polygon is 254 cm. 72 cm

12. Lesson Quiz Find each perimeter. 1. 2. 3. What is the perimeter of a rectangle with length 22 cm and width 8 cm? P=4s P=4(2.25) P=9cm 4 ft P=2l+2w P=2(22)+2(8) P = 44 + 16 P=60cm 5 6 __ Fractions!! Oh Noooooo Fractions!! Oh Noooooo 1 + 1 + 1 = 3 = 4

13. We will find the missing sides and perimeter of the irregular polygons. 17 ft. 25 ft. 5 ft. 5 ft 5 ft. b a c b = a = c = 25 ft 5 ft 10 + ? = 17 7 ft P = sum of the sides P = 17 + 2(25) + 5 + 7 + 5 + 5 +5 P = 94 ft.

14. 6m 14m 5m3m 2m 13m e d 7m 14 – 10 = 4cm P = sum of the sides P = 6 + 5 + 7 + 4 + 7 + 3 + 7 + 2 + 13 + 14 P = 68 cm

15. w 4w-5 Algebra in Geometry P = 2l + 2w P = 2(l + w) P = SOS P = 2(4w-5)+ 2w P = 2(4w-5 + w) P = w+w+4w – 5 + 4w - 5 Find the width of this rectangle if the perimeter is 70 units. P = 8w – 10 + 2w P = 2(5w-5) P = 10w - 10 P = 10w-10 70 = 10w - 10 +10 80 = 10w___ ____ 10 10 8 = width Now let’s check….. 70 = 2(8) + 2(4 ∙8 – 5) 70 = 16 + 2(32-5) 70 = 16 + 2(27) 70 = 16 + 54 70 = 70

16. Did we accomplish the objective? Did we find the perimeter of polygons? Did we find the missing side of polygons and then find the perimeter? We also completed a Challenge problem that shows how algebra and geometry work together.