Solving Area Problems Using Scale Drawings
Video solutions to help Grade 7 students solve area problems related to scale drawings and percent.
Plans and Worksheets for Grade 7
Plans and Worksheets for all Grades
Lessons for Grade 7
Common Core For Grade 7
New York State Common Core Math Grade 7, Module 4, Lesson 15
Lesson 15 Student Outcomes
• Students solve area problems related to scale drawings and percent by using the fact that an area, A', of
scale drawing is k2
times the corresponding area, A, in the original drawing, where k is the scale factor.
Lesson 15 Classwork
For each diagram, Drawing 2 is a scale drawing of Drawing 1. Complete the accompanying charts.
For each drawing: identify the side lengths, determine the area, and compute the scale factor.
Convert each scale factor into a fraction and percent, examine the results, and write a conclusion
relating scale factors to area.
Key Points: Overall Conclusion
If the scale factor is represented by k, then the area of the scale drawing is k2
times the corresponding area of the
What percent of the area of the large square is the area of the small square?
What percent of the area of the large disk lies outside the smaller disk?
If the area of the shaded region in the larger figure is approximately 21.5 square inches, write an equation that relates
the areas using scale factor and explain what each quantity represents. Determine the area of the shaded region in the
smaller scale drawing.
Use Figure 1 below and the enlarged scale drawing to justify why the area of the scale drawing is k2
times the area of the
Explain why the expressions (kl)(kw) and k2
lw are equivalent. How do the expressions reveal different information
about this situation?
1. The Lake Smith basketball team had a team picture taken of the players, the coaches, and the trophies from the
season. The picture was 4 inches by 6 inches. The team decides to have the picture enlarged to a poster and then
enlarged again to a banner measuring 48 inches by 72 inches.
a. Sketch drawings to illustrate the original picture and enlargements.
b. If the scale factor from the picture to the poster is 500%, determine the dimensions of the poster.
c. What scale factor is used to create the banner from the picture?
d. What percent of the area of the picture is the area of the poster? Justify your answer using the scale factor
AND by finding the actual areas.
e. Write an equation involving the scale factor that relates the area of the poster to the area of the picture.
f. Assume you started with the banner and wanted to reduce it to the size of the poster. What would the scale
factor as a percent be?
g. What scale factor would be used to reduce the poster to the size of the picture?
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.