Perimeter and Area

Lesson 1.5

Core Focus onRatios, Rates and Statistics

1. Determine whether or not each sequence is a geometric sequence. Explain your choice.

a) 2, 6, 18, 54, …

b) 2, 4, 6, 8, …

2. Complete each conversion.

a) 4 yards = _____ feet

b) 20 millimeters = _____ centimeters

Warm-Up

yes, the ratio is 3

12

2

no, the terms have a difference of 2

Perimeter and Area

Convert measurements to find perimeter and area.

Lesson 1.5

PerimeterThe total length around a shape. Add the lengths of the sides of the shape together to find the perimeter.

AreaThe 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.

Vocabulary

Explore! 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.

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.

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?

Find the perimeter of the rectangle in:

a. meters.

Add the lengths of all four sides.

The perimeter is .

3 3 14 4 2

2 2 5 meters

Example 1

12

5 meters

Remember to write the name of the units in your answer.

Find the perimeter of the rectangle in:

b. centimeters.

Convert meters to centimetersusing 1 meter = 100 centimeters.

Add the new lengths of all 200 + 75 + 200 + 75 = 550four sides.

The perimeter is 550 centimeters.

Example 1 Continued…

Find the area of the triangle in:

a. square feet

Use the area formula for a triangle.

Locate the length of the base b = 4and height. h = 3

Calculate the area.

The area is 6 square feet.

12 A b h

Example 2

12 4 3 6 A

Find the area of the triangle in:

b. square inches.

Convert feet to inches using b = 4 12 = 48 in1 foot = 12 inches. h = 3 12 = 36 in

Calculate the area using thenew lengths.

The area is 864 square inches.

Example 2 Continued…

12 48 36 864 A

One rectangle has sides twice as long as another rectangle.

a. Find the ratio of the smaller perimeterto 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 or 1 : 2to the larger perimeter.

Example 3

8 1

16 2

One rectangle has sides twice as long as another rectangle.

b. Find the ratio of the smaller area tothe 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 or 1 : 4to the larger area.

Example 3 Continued…

3 1

12 4

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?

Communication Prompt

1. Find the perimeter of the rectangle in yards.

2. Find the perimeter of the rectangle in feet.

3. Find the area of the rectangle in square yards.

4. Find the area of the rectangle in square feet.

2 yd

4 yd

Exit Problems

12 yards

36 feet

8 square yards

72 square feet