Digits, Grade 7, Volume 1, Homework Helper

4-4: Areas of Semicircles and Quarter Circles

Key Concept

A semicircle is one half of a circle.

Area of a semicircle equals , 1 half , middle dot (area of a circle)

equals , 1 half , pi , r squared

A semicircle with diameter 4 inches

A quarter circle is one fourth of a circle.

Area of a quarter circle equals , 1 fourth , middle dot (area of a circle)

equals , 1 fourth , pi , r squared

A semicircle with diameter 6 inches

Part 1

Example Finding Areas of Semicircles

Find the area of each shaded semicircle. Leave your answer in terms of π.

  • a. A semicircle with radius 4 inches

  • b. A semicircle with radius 4 inches

  • c. A semicircle with radius 4 inches

Solution

  • a. d = 4 in., so r = 2 in.

    table with 4 rows and 2 columns , row1 column 1 , cap areaofsemicircle , column 2 equals , 1 half , pi , r squared , row2 column 1 , , column 2 equals , 1 half , pi . open 2 close squared , row3 column 1 , , column 2 equals , 1 half , pi open 4 close , row4 column 1 , , column 2 equals 2 pi , end table

    The area of the semicircle is 2 π in.2.


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Table of Contents

Digits, Grade 7, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Expressions, Equations, and Relationships Unit C: Measurement and Geometry Unit D: Proportionality English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties