How can you use formulas to find the area and perimeter of shapes? Replace the unknowns with the length and the width.
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1 ? Name 9.1 Formulas for rea and Perimeter Essential Question How can you use formulas to find the area and perimeter of shapes? lgebraic Reasoning 5.4., 5.4.H MTHEMTIL PROESSES 5.1., 5.1.F Unlock the Problem formula is an equation that expresses a mathematical rule. You can use formulas to find the perimeter and area of rectangles. Lloyd is planting a rectangular garden that measures 40 feet by 24 feet. He wants to put a fence around it to protect his vegetables from rabbits. How many feet of fencing does he need? Use a formula to find the perimeter. P = l + w + l + w P = perimeter; l = length; w = width P = 40 + _ + _ + _ P = _ dd. Replace the unknowns with the lengths and the widths. The perimeter is _ feet. So, Lloyd needs _ feet of fencing. Lloyd needs to find how large his garden is so he can order enough mulch for the garden. What is the area of Lloyd s garden? Use a formula to find the area. Remember rea is measured in square units, such as square feet or sq ft. = l w _ = area; l = length; w = width Replace the unknowns with the length and the width. Multiply. So, the area of Lloyd s garden is _ square feet. Try This! You can also use the formula P = 2l + 2w to find the perimeter. What is the perimeter of a rectangle that is 12 feet long and 16 feet wide? P = 2 _ + 2 _ P = _ The perimeter is _ feet. Replace the unknowns with the length and the width. Math Talk Mathematical Processes Explain how you can use the properties of operations to rewrite P = l + w + l + w as P = 2l + 2w. Module 9 349
2 You can find the area of complex figures by separating them into two or more simpler shapes. Example Find the area. STEP 1 Separate the figure into a rectangle and a square. STEP 2 Find the area of the rectangle. = l w 4 m 5 m 3 m 3 m The area of the rectangle is _ square meters. STEP 3 Find the area of the square. The area of the square is _ square meters. STEP 4 Find the area of the complex figure by adding the areas. + _ So, the area of the complex figure is _ square meters. Share and Show 1. Find the perimeter of the square. 2. Find the area of the rectangle. 12 feet P = _ + _ + _ + _ P = _ The perimeter is _ meters feet _ The area is _ square feet.
3 Name Problem Solving 3. Explain how you can use s to write the formula for the perimeter of a square with side length s. 4. rectangle has an area of 96 square feet. If the length of the rectangle is 12 feet, what is the width of the rectangle? Problem Solving 5. rent plans to stain a deck that is 14 feet by 8 feet. If one can of stain covers an area of 100 square feet, how many cans of stain will he need? Explain. 6. Multi-Step Latoya uses 50 feet of wood to make a rectangular garden bed. If the length of the garden bed is 10 feet, what is the width? 7. What s the Error? Maggie wants to fence off two sideby-side sections of her garden. Each section is 14 feet long and 6 feet wide. She says she needs 80 feet of fencing. Explain what is wrong with her thinking. How much fencing does she really need? Module 9 Lesson 1 351
4 aily ssessment Task Mathematical Processes Fill in the bubble for the correct answer choice. 8. pply Tina is fixing a rectangular sign. She plans to place metal trim around the sign edges. The rectangle measures 32 inches by 9 inches. How much trim will Tina need? 36 inches 41 inches 72 inches 82 inches 9. rectangle has a length of 5 meters and a width of 4 meters. Which equation can you use to find the perimeter? P = 4 5 P = 4 4 P = P = Multi-Step Lana had an L shaped piece of felt. Her mom cut it into two rectangles. One rectangle measured 4 inches by 9 inches, and the other measured 4 inches by 3 inches. What is the total area of the two rectangles? 40 square inches 72 square inches 48 square inches 24 square inches TEXS Test Prep 11. Mai wants to tile the floor of her kitchen. Each tile has an area of 1 square foot. The floor of her kitchen is 11 feet by 16 feet. How many tiles does she need?
5 Homework and Practice Name lgebraic Reasoning 5.4., 5.4.H MTHEMTIL PROESSES 5.1., 5.1.F 9.1 Formulas for rea and Perimeter 1. Find the perimeter of the rectangle. 2. Find the area of the square. 15 feet 21 feet P = _ + _ +_ + _ P = _ The perimeter is _ feet. 17 inches _ The area is _ square inches. 3. rectangle has a perimeter of 68 inches. If the width of the rectangle is 10 inches, what is the length of the rectangle? Explain how you know. 4. square has an area of 81 square feet. What is the length of each side of the square? Explain how you know. Problem Solving 5. Lea wants to put a fence around her garden. Her garden measures 14 feet by 15 feet. She has 50 feet of fencing. How many more feet of fencing does Lea need to put a fence around her garden? 6. Lea wants to put a new layer of soil on her 14 feet by 15 feet garden. She finds the area of her garden so she knows how much soil to buy. If one bag of soil covers 20 square feet, how many bags of soil will Lea need? Explain. Module 9 Lesson 1 353
6 Lesson heck TEXS Test Prep Fill in the bubble completely to show your answer. 7. soccer field has a length of 100 yards and a width of 60 yards. Which equation can you use to find the area of the soccer field? 8. baseball diamond is a square with a perimeter of 360 feet. What is the length of one side? = = = = feet 180 feet 90 feet 60 feet 9. Zoey wants to cover her bedroom floor with carpet squares. Each square has an area of 1 square foot. Her bedroom measures 12 feet by 14 feet. How many carpet squares does Zoey need? Edward wants to put a string of lights around a rectangular window that is 32 inches wide and 40 inches high. How long will the string of lights need to be to go around the window? 72 inches 1,280 inches 144 inches 112 inches 11. Multi-Step hantal buys two small rugs for her kitchen. One rug measures 3 feet by 5 feet. The other rug measures 4 feet by 6 feet. What is the area of the part of the kitchen the two rugs will cover? 12. Multi-Step Isaac is painting a wall that is 9 feet by 18 feet. So far, he has painted a part of the wall that is a 4 feet by 7 feet rectangle. What is the area of the part of the wall that Isaac has left to paint? 39 square feet 190 square feet 30 square feet 134 square feet square feet 36 square feet 22 square feet 151 square feet
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