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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Lesson Plans and Worksheets for Grade 7

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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 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.