# Real-World Area Problems

Video solutions to help Grade 7 students learn how to determine the area of composite figures in real-life contextual situations using composition and decomposition of polygons and circular regions.

## New York State Common Core Math Grade 7, Module 6, Lesson 20

### Lesson 20 Student Outcomes

• Students determine the area of composite figures in real-life contextual situations using composition and decomposition of polygons and circular regions.

### Lesson 20 Summary

• The following are useful strategies when tackling area problems with real-world context:
• Decompose drawings into familiar polygons and circular regions, and identify all relevant
• Pay attention to the unit needed in a response to each question.

Lesson 20 Classwork

Opening Exercise
Find the area of each shape based on the provided measurements. Explain how you found each area.

Example 1
A landscape company wants to plant lawn seed. A lb. bag of lawn seed will cover up to sq. ft. of grass and costs plus the sales tax. A scale drawing of a rectangular yard is given. The length of the longest side is ft. The house, driveway, sidewalk, garden areas, and utility pad are shaded. The unshaded area has been prepared for planting grass.
How many lb. bags of lawn seed should be ordered, and what is the cost?

Exercise 1
A landscape contractor looks at a scale drawing of a yard and estimates that the area of the home and garage is the same as the area of a rectangle that is 100 ft. × 35 ft. The contractor comes up with 5,500 ft2. How close is this estimate?

Example 2
Ten dartboard targets are being painted as shown in the following figure. The radius of the smallest circle is in. and each successive, larger circle is in. more in radius than the circle before it. A “tester” can of red and of white paint is purchased to paint the target. Each oz. can of paint covers 16 ft2. Is there enough paint of each color to create all ten targets?

Lesson 20 Opening Exercise and Example 1

Lesson 20 Example 2
Lesson 22 Example 2
The square in this figure has a side length of inches. The radius of the quarter circle is inches.
a. Estimate the shaded area.
b. What is the exact area of the shaded region?
c. What is the approximate area using π = 22/7 ?

Lesson 20 Exit Ticket
A homeowner called in a painter to paint bedroom walls and ceiling. The bedroom is 18 ft. long, 12 ft. wide, and 8 ft. high. The room has two doors each 3 ft. by 7 ft. and three windows each 3 ft. by 5 ft. The doors and windows do not have to be painted. A gallon of paint can cover 300 ft2. A hired painter claims he will need 4 gal. Show that the estimate is too high.