Composite Area Problems

Examples, videos, and solutions to help Grade 7 students learn how to find the area of regions in the plane with polygonal boundaries by decomposing the plane into triangles and quadrilaterals, including regions with polygonal holes.

New York State Common Core Math Grade 7, Module 3, Lesson 20

Download worksheets for Grade 7, Module 3, Lesson 20

Lesson 20 Student Outcomes

• Students find the area of regions in the plane with polygonal boundaries by decomposing the plane into triangles and quadrilaterals, including regions with polygonal holes.
• Students find composite area of regions in the plane by decomposing the plane into familiar figures (triangles, quadrilaterals, circles, semi-circles, and quarter circles).

Lesson 20 Classwork

Example 1
Find the composite area of the shaded region. Use 3.14 for π.

Exercise 1
A yard is shown with the shaded section indicating grassy areas and the unshaded sections indicating buildings or paved areas. Find the area of the space covered with grass in units².

Example 2
Find the area of the figure which consists of a rectangle with a semicircle on top. Use 3.14 for π.

Exercise 2
Find the area of the shaded region using π = 3.14.

Example 3
Find the area of the shaded region.

Exercise 3
Find the area of the shaded region.

• Show Step-by-step Solutions

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.