# Composite Area Problems

Video 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.

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Lessons for Grade 7
Common Core For Grade 7
## New York State Common Core Math 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 units

^{2}.

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.