Length GH 8 2 6 Ruler Postulate Postulate 11 Width GK 7 2 5 Ruler Postulate

Length gh 8 2 6 ruler postulate postulate 11 width gk

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Length GH = 8 2 = 6 Ruler Postulate (Postulate 1.1) Width GK = 7 2 = 5 Ruler Postulate (Postulate 1.1) The shed has a length of 6 feet and a width of 5 feet. Step 2 Substitute the values for the length and width into the formula for the area of a rectangle. A = w Write the formula for area of a rectangle. = ( 6 )( 5 ) Substitute. = 30 Multiply. So, the area of the floor of the shed is 30 square feet. 4. Look Back Make sure your answer makes sense in the context of the problem. Because you are finding an area, your answer should be in square units. An answer of 30 square feet makes sense in the context of the problem. Monitoring Progress Help in English and Spanish at BigIdeasMath.com 11. You are building a patio in your school’s courtyard. In the diagram at the left, the coordinates represent the four vertices of the patio. Each unit in the coordinate plane represents 1 foot. Find the area of the patio. 1 ft 1 ft x y 2 M (2, 2) R (2, -3) P (6, -3) N (6, 2)
34 Chapter 1 Basics of Geometry Tutorial Help in English and Spanish at BigIdeasMath.com Exercises 1.4 1. COMPLETE THE SENTENCE The perimeter of a square with side length s is P = ____. 2. WRITING What formulas can you use to find the area of a triangle in a coordinate plane? 3. 4. 5. 6. In Exercises 7–12, find the perimeter of the polygon with the given vertices. (See Example 2.) 7. G (2, 4), H (2, 3), J ( 2, 3), K ( 2, 4) 8. Q ( 3, 2), R (1, 2), S (1, 2), T ( 3, 2) 9. U ( 2, 4), V (3, 4), W (3, 4) 10. X ( 1, 3), Y (3, 0), Z ( 1, 2) 11. x y 4 2 4 2 2 4 L (1, 4) M (4, 0) N (2, 0) P ( 1, 2) 12. x y 2 4 2 4 A (0, 4) D (0, 2) E ( 2, 2) F ( 2, 4) B (2, 0) C (2, 2) In Exercises 13–16, find the area of the polygon with the given vertices. (See Example 3.) 13. E (3, 1), F (3, 2), G ( 2, 2) 14. J ( 3, 4), K (4, 4), L (3, 3) 15. W (0, 0), X (0, 3), Y ( 3, 3), Z ( 3, 0) 16. N ( 2, 1), P (3, 1), Q (3, 1), R ( 2, 1) In Exercises 17–24, use the diagram. x y 4 2 4 6 2 4 6 2 2 4 B (0, 3) A ( 5, 4) F ( 2, 1) E (2, 3) D (4, 5) C (4, 1) 17. Find the perimeter of CDE. 18. Find the perimeter of rectangle BCEF. 19. Find the perimeter of ABF. 20. Find the perimeter of quadrilateral ABCD. 21. Find the area of CDE. 22. Find the area of rectangle BCEF. 23. Find the area of ABF. 24. Find the area of quadrilateral ABCD. Monitoring Progress and Modeling with Mathematics
Section 1.4 Perimeter and Area in the Coordinate Plane 35 ERROR ANALYSIS In Exercises 25 and 26, describe and correct the error in finding the perimeter or area of the polygon. 25. 26. A (4, 3) B (5, 1) C (1, 1) x y 2 4 2 2 6 4 b = 5 1 = 4 h = —— (5 4) 2 + (1 3) 2 = 5 2.2 A = 1 2 bh 1 2 (4)(2.2) = 4.4 The area is about 4.4 square units. In Exercises 27 and 28, use the diagram. x y 2 2 2 2 Q (2, 1) P ( 2, 1) 27. Determine which point is the remaining vertex of a triangle with an area of 4 square units. A R (2, 0) B S ( 2, 1) C T ( 1, 0) D U (2, 2) 28. Determine which points are the remaining vertices of a rectangle with a perimeter of 14 units. A A (2, 2) and B (2, 1) B C ( 2, 2) and D ( 2, 2) C E ( 2, 2) and F (2, 2) D G (2, 0) and H ( 2, 0) 29. USING STRUCTURE Use the diagram. x y 4 2 4 2 2 K (4, 4) L (4, 0) H (2, 0) G (2, 2) J (0, 4) E (0, 0) F (0, 2) a. Find the areas of square EFGH and square EJKL . What happens to the area when the perimeter of square EFGH is doubled? b. Is this true for every square? Explain. 30. MODELING WITH MATHEMATICS You are growing zucchini plants in your garden. In the figure, the entire garden is rectangle QRST . Each unit in the coordinate plane represents 1 foot. (See Example 4.) R (7, 13) Q (1, 13) U (1, 4) T (1, 1) S (7, 1) W (4, 1) V (4, 4) x y 4 2 6 8 10 12 14 4 2 8 6 10 a. Find the area of the garden. b. Zucchini plants require 9 square feet around each plant. How many zucchini plants can you plant? c. You decide to use square TUVW to grow lettuce. You can plant four heads of lettuce per square foot. How many of each vegetable can you plant? Explain. x y 4 2 2 4 2 P = 2 + 2 w = 2(4) + 2(3) = 14 The perimeter is 14 units.
36 Chapter 1 Basics of Geometry 31. MODELING WITH MATHEMATICS You are going for a hike in the woods. You hike to a waterfall that is 4 miles east of where you left your car. You then hike to a lookout point that is 2 miles north of your car. From the lookout point, you return to your car. a. Map out your route in a coordinate plane with your car at the origin. Let each unit in the coordinate plane represent 1 mile. Assume you travel along straight paths. b. How far do you travel during the entire hike? c. When you leave the waterfall, you decide to hike to an old wishing well before going to the lookout point. The wishing well is 3 miles north and 2 miles west of the lookout point. How far do you travel during the entire hike? 32. HOW DO YOU SEE IT? Without performing any calculations, determine whether the triangle or the rectangle has a greater area. Which one has a greater perimeter? Explain your reasoning. x y 4 4 2 2 4 33. MATHEMATICAL CONNECTIONS The lines y 1 = 2 x 6, y 2 = 3 x + 4, and y 3 = 1 2 x + 4 are the sides of a right triangle. a. Use slopes to determine which sides are perpendicular. b. Find the vertices of the triangle. c. Find the perimeter and area of the triangle. 34. THOUGHT PROVOKING Your bedroom has an area of 350 square feet. You are remodeling to include an attached bathroom that has an area of 150 square feet. Draw a diagram of the remodeled bedroom and bathroom in a coordinate plane. 35. PROBLEM SOLVING Use the diagram. x y 3 1 3 1 1 3 M (2, 2) N (2, 2) P ( 2, 2) L ( 2, 2) a. Find the perimeter and area of the square. b. Connect the midpoints of the sides of the given square to make a quadrilateral. Is this quadrilateral a square? Explain your reasoning. c. Find the perimeter and area of the quadrilateral you made in part (b). Compare this area to the area you found in part (a).

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