Math Tech 1 Unit 11 Perimeter, Circumference and Area Name Pd
11-1 Perimeter Perimeter - Units - Ex. 1: Find the perimeter of a rectangle with length 7 m and width 5 m. Ex. 2: Find the perimeter of the following irregular shape 5 in 4 in 8 in 6 in PSSA Example: An irregular figure is constructed below. 1 cm 5 cm y 4 cm 4 cm 6 cm x a) Find the length of side x and side y. Explain in words how you found your solution. b) Using your answer from part a), find the perimeter of the shape.
11-1 Perimeter Find the perimeter of each figure. - 1 -
11-1 Perimeter Compute the length of x in each figure. - 2 -
11-2 Circumference Definition of. Circumference - Formula: Ex. 1: Find the circumference of a circle with r = 6 in. Ex. 2: Given that d = 6 2 cm, find the radius and the circumference. Ex. 3: Given the circumference equals 37.7 m, find the radius of the circle. PSSA Example: If the sum of the diameter and radius of a circle is 9 inches, find the circumference of the circle. Explain in words how you found your solution.
11-2 Circumference - 3 -
11-3 Perimeter of Irregular Shapes Ex. 1: In the accompanying diagram, a figure is constructed of a semi-circle on top of an equilateral triangle. If the length of a side of the triangle is 3 inches, find the perimeter of the figure. Ex. 2: Suppose a figure is formed by placing a semi-circle of diameter 6 m on top of a semi-circle of diameter 5 m. Find the perimeter of the resulting figure. PSSA Example: A Norman window is a window that has a semi-circle on top of a rectangle, where the diameter of the semi-circle and the width of the rectangle are the same. Suppose a Norman window has a width of 2 feet and a length of 4 feet. How much wood should be bought to wrap around the frame of the window? In words, explain how you found your solution. 2 ft 4 ft
11.1-11.3 Classwork - 4 -
11.1-11.3 Classwork - 5 -
11-3 Irregular Shapes Find the perimeter of each figure. Round to the nearest tenth. - 6 -
11-3 Irregular Shapes 1) Calculate the perimeter of the figure. 2) A track around a soccer field is shown below. All measurements represent distance in feet. Find the distance a jogger runs for one lap around the track. 3) Wooden molding surrounds the outside of the window. Find the length of the molding. 4) The Figure contains a square on top of a semi-circle. Find the perimeter. 6 in - 7 -
11-3 Irregular Shapes 5) Find the perimeter of the following figure. It consists of 6 equilateral triangles. Each side is 6 cm. 6) Find the perimeter of the baseball diamond. It consists of 2 sides of equal length and one-quarter of a circle. 7) How long is the Equator? The radius of the Earth is 4000 miles. 8) What is the perimeter of a football field? The field is 360 feet by 150 feet. - 8 -
11-3 Irregular Shapes 9) Interstate 495 is a circular beltway around Washington D.C. If the radius of D.C. is 15 miles, how long is the beltway? 10) If a stained-glass window consists of a square of length 2 feet, with a semi-circle on each side of the square, what is the perimeter of the window? - 9 -
11-4 AREA OF SQUARES, RECTANGLES, AND PARALLELOGRAMS Area is the number of square units it takes to completely cover the figure your finding the area of. A. AREA IS ALWAYS MEASURED IN SQUARE UNITS. 1 SQ. CM. OR 1 CM 2 1 SQ. IN. OR 1 IN 2 1 SQ. FT. OR 1 FT 2 B. FORMULAS SQUARE A = s* s or s 2 s s RECTANGLE A = l * w w l PARALLELOGRAM A = b * h h b
C. Examples: Find the area and perimeter of each parallelogram. 1. 5 cm 2. Square s = 11 mm 3 cm 3. Find the area and perimeter of RSTU. 24 in R 30 S U 32 in T 4. The Mesko s are planning to sod some parts of their yard. Find the number of square yards of grass needed. 200 ft Vegetable Garden 40 ft 150 ft 50 ft 50 ft 100 ft 60 ft garage House and walkways
11-4 Classwork Find the perimeter and area of the figure. Round to the nearest tenth if needed. Do not forget units! 1. 2. 5in h 16 ft h =(16 2) x 3 7in 23 ft P= P= A= A= 3. If the base of a rectangle is 15 cm and the area is 330 cm 2, what is the height of the rectangle? 4 If the perimeter of a square is 4cm, what will the perimeter be if the length of each side is doubled? a. 64 cm b. 16 cm c. 8 cm d. 6 cm - 10 -
5. Charlene helps to construct stages for concerts. She needs to increase the size of the stage shown below. l w Charlene plans to create a new stage by doubling l, the length, and doubling w, the width, of the original stage. Which of these could represent the area of the new stage? a. lw b. 2lw c. 4lw d. 8lw 6. Find the area and the perimeter of the figure. 10 m 9 m 13 m 3 m P = A = - 11 -
11-4 Homework H = (24 2) x 3-12 -
11-5 AREA OF TRIANGLES, TRAPEZOIDS, AND RHOMBI Recall the area of a square, rectangle, or parallelogram is b*h A triangle is half a square, rectangle, or parallelogram h h b b b h TRIANGLE A = ½ b*h or A = b * h 2 A trapezoid is a quadrilateral with exactly one pair of opposite sides parallel The parallel sided are called bases The non-parallel sides are called legs TRAPEZOID A = ( b + b ) 2 2 1 h b 2 b 1 h A rhombus is a parallelogram with all sides congruent and opposite sides parallel RHOMBUS d 1 d A bh or A = 2 2 = d 1 d 2
Examples: Find the area of each figure. Round to the nearest tenth if necessary. 1. 2. 6 in 5 in 8 in 12 ft 8ft 18 ft 9 in 20 ft 3. 20ft 30ft 30ft 20ft 4. Find the area of quadrilateral ABCD if AC=35, BF=18, and DE=10. B A E F D C 5. Rhombus RSTU has an area of 64 square inches. Find US if RT=8 inches R S U T
6. Trapezoid DEFG has an area of 120 square feet. Find the height of DEFG. D 10 ft E G 20 ft F 7. This stained glass window is composed of 8 congruent trapezoidal shapes. The total area of the design is 72 square feet. Each trapezoid has bases of 3 and 6 feet. Find the height of each trapezoid
11-5 Classwork Find the area of the figure. 1. 2. 22.9 cm 17.7 cm 25 m 17 m 18 m 3. What is the area of a triangle with base 26.8 mm and height 12.7 mm? Find the missing measurement of the trapezoid. 4. height =.75 mm 5. height = b 1 = 1.3 mm b 2 = 5.7 mm b 1 = 10 mm b 2 = 12 mm area = area = 66 mm 2-13 -
6. A triangle has been drawn on the unit grid below. What is the area of the triangle? a. 5 square units b. 6 square units c. 7 square units d. 10 square units 7. The sail on a boat is triangular and required 540 ft 2 of nylon to make. If the base of the sail is 36 feet, find its height. - 14 -
11-5 Homework d 1 = [(12 2)x 3 ] x 2 d 2 = [12 2] x 2 16 48 7. The area of a trapezoid is 144 in 2. One of the bases is 8 in and the other base is 10 in. find the height of the trapezoid. 8. The area of a rhombus is 80 m 2. One of the diagonals is 20 m. What is the length of the other diagonal? - 15 -
11-6 AREA OF CIRCLES CIRCLE - a set of points equidistant from a common point The common point is called the center of the circle RADIUS distance from center to the side of the circle DIAMETER distance across circle through the center CIRCUMFERENCE distance around the circle π number used to calculate circumference and area of a circle π 3.14 AREA CIRCUMFERENCE Radius 2 * pi diameter * pi or 2*radius*pi A = πr 2 C = dπ C=2rπ Examples: Complete the table. Radius Diameter Area Circumference 1. 5 km 2. 16π in2 3. 16m 4. 121π m
5. Find the area of the figure. 12 cm 16 cm 6. Find the area of the shaded region. 10 ft 5 ft 7. 20 in
11-6 Classwork 1. Parallelogram 17 ft 5 ft base height Area Perimeter 2. Rectangle 24 cm 216 cm 2 3. Square 1600 ft 2 Find the area 4; 6 km 5. Find the area and circumference of a circle with diameter 4.8 m. 6. You are presented with a gold plated hula-hoop. The presenter tells you that it is worth about $62.62 per inch of length. If the diameter of the hula-hoop is twenty-seven inches, how much is it worth? - 16 -
11-6 Area or Circles b = 5.2 in h = 4.5 in b = 13.9 ft h = 12 ft Find the area of each circle. Round to the nearest tenth. 11. A circle with a radius of 6 yards 12. A circle with a diameter of 18 millimeters 13. A circle with a diameter of 26 feet. 14. A circle with a circumference of 88 kilometers - 17 -
11-7 Areas of Irregular Figures Examples: Find the area of the figures in square feet. Round to the nearest tenth if necessary. 1. 32 ft 16 ft 15 ft 2. 12 8 3. 25 ft 100 ft Rose Garden 20 ft 25 ft Lawn
11.5-11.7 Classwork DIRECTIONS: Round all answers to the nearest tenth. I. Area of Parallelograms A = bh Formula: 1. 2. 3. 4. 5. The Kanes are planning to plant grass on some parts of their yard. Find the number of square yards of grass needed. II. Area of Triangles, Trapezoids, and Rhombi Formula Triangle: A = ½ bh Formula Trapezoid: A = ½ h(b 1 + b 2 ) Formula Rhombus: A = ½ d 1 d 2 1. 2. Rhombus RSTU has an area of 64 square inches. Find US if RT = 8 in. - 18 -
3. Trapezoid DEFG has an area of 120 square feet. Find the height of DEFG. III. Circles Circumference formula: C = 2π r Area Formula: A = π r 2 1. Find the area of a circle with circumference 20Π. 2. Find the circumference of a circle with area of 144Π. Find the area of the shaded regions. 3. 4. 5. IV. Irregular Figures. Find the area of each figure. 1. 2. 3. - 19 -
11-7 Homework - 20 -
Review Perimeter/Circumference/Area Name: Find the perimeter or circumference of each figure. 1. 2. d=.12 m 12 dm P 9 dm S 3. 4. 8 mm 5 mm R 7 mm T Q 6 dm R 2 dm S 13 ft H 8 dm T U 4 dm 5. Find the cost of fencing the yard pictured. The fencing costs $1.45 per meter. 17 m 11 m 15 m 6. The circumference of a pipe is 42 cm. Find its diameter. 19 m Calculate the area of the following figures. 7. 12.5 dm 8. R S 11 in V 8 dm 16.3 dm T 16.5 in 20 in 9. A circle with r= 5.7 cm 10. L M 3.5 m P 16.3 m N - 21 -
Calculate the area of the following figures. 11. A triangle with base 26.8 m and height 12.7 m 12. 9 ft 13 ft 13. A circle with d= 16.4 m 14. 25 m 17 m 18 m Explain and Show All Your Work. 15. The Woodland Hills Track team wanted to paint the inside of the track Wolverine blue. Using the diagram below and knowing that a gallon of paint will cover 25 m 2 how many gallons of paint will they need? 400 m 37 m Find the perimeter/circumference and area of each figure. Show all formulas, work and units. 16. 5 in.. 17. each step is the same size 9 5 in.. 9 Find the area of the shaded regions. Show all formulas, work and units. 18. 19. 21 cm. 9 cm. 16 cm. 5 cm. - 22 -