Lesson 1 5 Core Focus on Ratios Rates

Lesson 1. 5 Core Focus on Ratios, Rates and Statistics Perimeter and Area

Warm-Up 1. Determine whether or not each sequence is a geometric sequence. Explain your choice. a) 2, 6, 18, 54, … yes, the ratio is 3 b) 2, 4, 6, 8, … no, the terms have a difference of 2 2. Complete each conversion. a) 4 yards = _____ 12 feet b) 20 millimeters = _____ 2 centimeters

Lesson 1. 5 Perimeter and Area Convert measurements to find perimeter and area.

Vocabulary Perimeter The total length around a shape. Add the lengths of the sides of the shape together to find the perimeter. Area The number of square units that fit inside the shape. Good to Know! There are times when it will be necessary to convert from one unit of measurement to another when finding area or perimeter.

Explore! The Patio Trent and Mandy put a rectangular patio in their back yard. They plan to put a fence around the patio. They will use square tiles that are 1 meter by 1 meter to fill in the patio. Step 1 Find the perimeter of the patio so Trent and Mandy know how much fencing to buy. Your answer should be in meters. Step 2 Find the area of the patio. Your answer should be in square meters.

Explore! The Patio Step 3 Convert the measurements of each tile to centimeters. a. Find the perimeter of the patio in centimeters. b. Find the area of the patio in square centimeters. Step 4 Find the ratio of the perimeter of the patio in meters to the perimeter of the patio in centimeters. Step 5 Find the ratio of the area of the patio in meters to the area of the patio in centimeters. Step 6 Are the ratios from Steps 4 and 5 equal? Why or why not?

Example 1 Find the perimeter of the rectangle in: a. meters. Add the lengths of all four sides. The perimeter is . Remember to write the name of the units in your answer.

Example 1 Continued… Find the perimeter of the rectangle in: b. centimeters. Convert meters to centimeters using 1 meter = 100 centimeters. Add the new lengths of all four sides. The perimeter is 550 centimeters. 200 + 75 + 200 + 75 = 550

Example 2 Find the area of the triangle in: a. square feet Use the area formula for a triangle. Locate the length of the base and height. Calculate the area. The area is 6 square feet. b=4 h=3

Example 2 Continued… Find the area of the triangle in: b. square inches. Convert feet to inches using 1 foot = 12 inches. Calculate the area using the new lengths. The area is 864 square inches. b = 4 12 = 48 in h = 3 12 = 36 in

Example 3 One rectangle has sides twice as long as another rectangle. a. Find the ratio of the smaller perimeter to the larger perimeter. Find the perimeter of the smaller rectangle. 1 + 3 + 1 + 3 = 8 cm Find the perimeter of the larger rectangle. 2 + 6 + 2 + 6 = 16 cm Write the ratio of the smaller perimeter to the larger perimeter. or 1 : 2

Example 3 Continued… One rectangle has sides twice as long as another rectangle. b. Find the ratio of the smaller area to the larger area. Find the area of the smaller rectangle. 3 1 = 3 square centimeters Find the area of the larger rectangle. 6 2 = 12 square centimeters Write the ratio of the smaller area to the larger area. or 1 : 4

Communication Prompt For a square that is 1 centimeter by 1 centimeter, how do you find: a) its perimeter in terms of millimeters? b) its area in terms of square millimeters?

Exit Problems 2 yd 1. Find the perimeter of the rectangle in yards. 12 yards 2. Find the perimeter of the rectangle in feet. 36 feet 3. Find the area of the rectangle in square yards. 8 square yards 4. Find the area of the rectangle in square feet. 72 square feet 4 yd