To calculate the area of the figure.
Answer to Problem 11PPS
Explanation of Solution
Given information:
The figure is can be divided into a square and four equal semicircles.
The length of the side of the square
That is,
Formula used: Area of a square
Area of semicircle
For calculations,
Calculation:
On noticing the placement of the semicircles and the square, it is observed that the side of the square is twice the radius of the semicircle.
That is,
Thus, it can be said that
Is the same as
Replacing the value of ‘a’ by twice ‘r’.
On further simplification.
On dividing the right-hand side numbers.
And, ‘a’ would be equal to.
Replacing the value of ‘r’.
Now, find the area of the shapes that constitute the composite figure mentioned in the problem.
Area of the square.
Putting the value of ‘a’ in this formula.
On solving this.
Area of semicircle
Formula for area of semicircle.
Now, since all the 4 semicircles have the same radius, multiple the area of one semicircle with 4. This will get the value of all the 4 semicircles.
Putting the values in the formula
Simplify the expression
On further calculation,
Dividing the numerator by the denominator.
Now, add the two areas to get the area of the given figure.
Putting values of the two areas.
It becomes
After rounding this to the nearest tenth
Chapter 11 Solutions
Pre-Algebra Student Edition
Additional Math Textbook Solutions
College Algebra (6th Edition)
Linear Algebra with Applications (2-Download)
College Algebra (7th Edition)
College Algebra (5th Edition)
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education