1. 1.8 Perimeter, Circumference, and Area SOL G11 & G14 Objects: TSW … find the perimeter or circumference of basic shapes. find the area of basic shapes.

2. Perimeter Is the sum of the length of its sides Area Number of square units it encloses Circumference The distance around a circle

3. Perimeter and Area of a Rectangle A is Area, P = Perimeter b is the base h is the height P = 2b + 2h units A = bh units 2 Example: find the area and perimeter of 10 15 b h P =2(15) + 2(10) =50 units A =(15) (10) =150 units 2

4. Example 1: The botany club members are designing a rectangular garden for the courtyard of your school. They plan to place edging on the outside of the path. How much edging material will they need? Width = 4 + 16 + 4 = 24 ft. Length = 4 + 22 + 4 = 30 ft. P = 2(b) + 2(h) = 2(24) + 2(30) = 108ft. They will need a 108ft. of edging to go around the courtyard.

5. Perimeter and Area of a Square A is Area, P = Perimeter s is side length P = 4s units A = s 2 units 2 Example: find the area and perimeter of 10 s P =4(10) =40 units A =(10) 2 =100 units 2

6. Perimeter and Area of a Triangle A is Area, P = Perimeter a, b, and c side length Base b, and height h P = a + b + c units A = ½ bh units 2 Example: find the area and perimeter of c P =13 + 8 + 17 =38 units A =½ (17)(6) =51 units2 a h b 8 13 6 17

7. Circumference and Area of a Circle A is Area, C = Circumference radius r, and diameter d C = πd, or C = 2πr A = πr 2 units 2 Example: find the area and circumference of C = 8π ≈8π ≈ 25.13 units A = π 4 2 = 50.27 units 2 r d 4 8 C = 2 π( 4) ≈ 25.13 units 16 π ≈

8. Example 2: What is the circumference of the circle in terms of π ? What is the circumference of the circle to the nearest tenth? A.) M B.) T C = πd = 15π units = 47.1238898 units ≈ 47.1 units C = 2πr = 2π(4) units = 8π units = 25.13274123 units ≈ 25.1 units

9. Got It? 2.) a.) What is the circumference of a circle with radius 24 m in terms of π ? b.) What is the circumference of a circle with diameter 24 m to the nearest tenth? C = πd = 24π m = 75.39822369 m ≈ 75.4 m C = 2πr = 2π(24) m = 48π m

10. Example 3: What is the perimeter of EFG? EF = 8 units GF = 6 units GE = (-3 – 3) 2 + (-2 – 6) 2 = (-6) 2 + (-8) 2 = 36 + 64 = 100 = 10 units P = 8 + 6 + 10 = 24 units

11. Got It? 3.) Graph quadrilateral JKLM with vertices J(-3, -3), K(1, -3), L(1, 4), and M(-3, 1). What is the perimeter of JKLM? LK = 7 units JK = 4 units JM = 4 units ML = (-3 – 1) 2 + (1 – 4) 2 = (-4) 2 + (-3) 2 = 16 + 9 = 25 = 5 units P = 7 + 4 + 4 + 5 = 20 units

12. Example 4: You want to make a rectangular banner similar to the one at the right. The banner shown is 2 ½ ft wide and 5 ft high. To the nearest square yard, how much material do you need? Convert the measurements to yards: Width: ft. = yd 5252 1 yd 3 ft 5656 1 yd 3 ft 5353 Height: 5 ft. = yd 5353 25 18 Area: yd yd = yd 5656 I will need 2 yd 2 of material

13. Got It? 4.) You are designing a poster that will be 3 yd wide and 8 ft high. How much paper do you need to make the poster? Give your answer in square feet. Convert the measurement to feet: Width: 3 yds = 9 ft Height: 8 ft. Area: 9(8) ft 2 = 72 ft 2

14. Example 5: What is the area of K in terms of π ? A = π r 2 = π 8 2 = 64 π m 2 Got It? 5.) The diameter of a circle is 14 ft. a.) What is the area of the circle in terms of π? b.) What is the area of the circle using an approximation of π? A = π r 2 = π 7 2 = 49 π units 2 49 π ft 2 ≈ 153.93804 ft 2

15. Postulate 1.10: Area Addition Postulate The area of a region is the sum or the areas of its nonoverlapping parts. Example 6: Rect. 1: 3(3) = 9 cm 2 Rect. 2: 3(6) = 18 cm 2 Rect. 3: 3(9) = 27 cm 2 Total Area 54 cm 2

16. Example 7: What is the area of the figure? Square: 4 2 = 16 ft 2 Rect.: 4(8) = 32 ft 2 Triangle: ½ 8(4) = 16 cm 2 Total Area = 16 + 32 + 16 = 64 ft 2