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Name: _____________________________________________ Period: ______ Packet 5: Perimeter and Area Perimeter The perimeter of a polygon is the sum of the lengths of the sides of the polygon. Think of a police show when they “have the perimeter surrounded”. Perimeter is only the outside! Perimeter means add up all the sides. For a circle, we call the perimeter “circumference”. Perimeters and Lengths are measured in feet, inches, meters, etc. Area The Area of a figure is the number of square units needed to cover a surface. Think of an area rug. Areas are measured in square feet, square inches, square meters, etc. Area covers the inside! AREA Formula CIRCUMFERENCE (Perimeter) Formula Circle A = r2 C = d or C = 2 r POLYGON AREA Formula 1 AREA Formula 2 Square A = s2 A = ½ d2 Rhombus A = bh A = ½ d1 d 2 Parallelogram A = bh Rectangle A = lw or A = bh Triangle A = ½ bh Trapezoid A = ½ h( b 1 + b2 ) Find the perimeter of the following figures. 1. 2. 3. 4. 5. 6. 7. 8. Find the exact value for area of each of the following figures. Make sure that you start by writing down the formula and then show ALL of your work!!! 1. A = ______ 2. A = ______ 3 3 10 5 3. A = ______ 8 4. A = ______ 6 6 8 5. A = ______ 6. A = ______ 4 4 20 7. A = ______ 4 10 Area of Shaded Figures Sometimes you need to find the area of an odd-shaped figure. We can use our knowledge of area of polygons and circles to help us find the area of an odd-shaped figure. Distance Formula Distance: in the coordinate plane given points (x1, y1) and (x2, y2) Distance Formula d ( x 2 x1 ) 2 ( y 2 y1 ) 2 1. (-2, 4) and (3, 4) 2. (-3, 9) and (-3, 13) 3. (3, 2) and (0, 2) 4. (8, -3) and (8, -4) 5. (-7, -1) and (-11, -1) 6. (-1, -1) and (-1, -2) 7. (8, -3) and (13, -3) 8. (13.3, 2.7) and (1.8, -1.8) 9. (-4, 8) and (-4, 11) 10. (-6, 6) and (-6, 10) 11. (21, 2) and (18, 16) 12. (-9.1, -6.3) and (-10.8, -20.6) 13. (11, -3.9) and (17.2, -0.2) 14. (23, 19) and (21, 31) 15. (2, 8) and (0, 8) 16. (4.3, -22.7) and (10.5, -35.9) 17. (-17.5, 11.7) and (-32.2, 2.3) 18. (2.8, 3.3) and (-7.4, 1) Use the Distance Formula to find the lengths of sides in order to find the area of the figure. 1. Find the area of the square whose vertices are (4, 7), (1, 7), (1, 3), and (4, 3) 2. Find the area of the trapezoid whose vertices are (-6, 3), (5, 0), (5, 3), and (0, 0) 3. Find the area of the triangle whose vertices 4. Find the area of the quadrilateral whose are vertices are (-9, 8), (-9, 16), and (-17, 8) (1, 4), (-5, 0), (7, -3), and (-1, -8) 5. Find the area of the trapezoid whose vertices are (-7, -4), (-7, 1), (0, -4), and (-4, 1) 6. Find the area of the triangle whose vertices are (6, 4), (3, 4), and (6, 1) 7. Find the area of the parallelogram whose vertices are (0, -1), (0, -4), (5, -1), and (5, -4) 8. Find the area of the quadrilateral whose vertices are (-3, -10), (-5, -1), (2, -1), and (-1, 3) 9. Find the area of the triangle whose vertices 10. Find the area of the trapezoid whose are vertices are (-7, 1), (1, -7), and (-7, -7) (8, -4), (3, -8), (16, -8), and (3, -4) 11. Find the area of the square whose vertices 12. Find the area of the quadrilateral whose are vertices are (-1, -5), (-8, -5), (-1, -2), and (-8, -2) (-5, -10), (-2, 3), (-8, -1), and (2, -3) 13. Find the area of the trapezoid whose vertices are (8, 5), (1, 5), (16, 9), and (1, 9) 14. Find the area of the parallelogram whose vertices are (-5, 11), (-8, 11), (-8, -1), and (-5, -1) 15. Find the area of the triangle whose vertices are (-2, 4), (1, 8), and (-2, 8) 16. Find the area of the quadrilateral whose vertices are (-6, -2), (-4, -11), (2, -3), and (-1, 2) 17. Find the area of the trapezoid whose vertices are (2, 0), (2, 7), (-14, 0), and (-6, 7) 18. Find the area of the quadrilateral whose vertices are (-5, -2), (-7, 5), (0, 1), and (-3, 8) Find the Side Given Perimeter or Area When working with problems involving formulas follow these steps: 1. Select the appropriate formula. 2. Plug in given information. 3. Solve for unknown. 4. Label answer. 5. Look back. 1. If the area is 141.9 m2, what is the 2. The area of a circle is 78.5 sq. cm. What height? is the radius of the circle? (Use 3.14 for π). 3. The circumference of a circle is 208π. Find the diameter. 4. The perimeter of a rectangle is 165 ft. The height of the rectangle is 39 ft. Find the length of the base of the rectangle. 5. The perimeter of the following figure is 40 ft. Find the value of x. 6. The area of the following figure is 60 ft2. Find the value of x. x+8 x+3 x 5 Find the area and perimeter of the following triangles. (Remember for right triangles to use a2 + b2 = c2) 1. 12 2. 15 x 8 6 6 12 Word Problems 1. The spray from a spinning lawn sprinkler makes a circle with a 40’ radius, what is the circumference and area of the circle? 2. Gears on a bicycle are just circles in shape. One gear has a diameter of 4”, and a smaller one has a diameter of 2”. How much bigger is the circumference of the larger one compared to the smaller one? 3. If a triangular sail has a vertical height of 83 ft and horizontal length of 40 ft, what is the area of the sail? 4. If the area of a small pizza is 78.5 in2, what size pizza box would best fit the small pizza? (Note: Pizza boxes are measured according to the length of one side.) 5. A rectangular field is to be fenced in completely. The width is 28 yd and the total area is 1,960 yd2. What is the length of the field? 6. Grace is making a display board for the school talent show. The display board is a 6 ft by 11 ft rectangle. She needs to add a ribbon border around the entire display board. What is the length of ribbon that she needs? 7. The perimeter of a rectangular field is 40 ft and its width is 10 ft. Find the area of this field. 8. Tammy needs to rent an office building. He needs 10,000 square feet of space. If Tammy found a building to rent that is 81 feet by 102 feet, is this building large enough to meet Tammy’s building needs? 9. Sara wants to buy wood to make a frame for her picture. Her picture is a 12” by 10” rectangle. What is the total length of the wood strips she will need for her project? 10. A certain wall is 13’ by 9’. A can of paint will cover 50 square feet. Will it be enough? Explain.