   Chapter 8.CR, Problem 31CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Find the exact areas of the shaded regions in Exercises 27 to 31. To determine

To find:

The exact areas of the shaded regions.

Explanation

Calculation:

Consider the following diagram as shown below:

ABC is the equilateral triangle.

In equilateral triangle, the circle touches at the midpoint of the sides of the triangle.

In equilateral triangle, the median passes through the origin of the circle and origin becomes centroid of the triangle.

Centroid divides the median in ration 2:1 from the vertex.

In equilateral; triangle, the median becomes perpendicular bisector of the triangle.

That is BD¯=DC¯

BC¯=BD¯+DC¯10=2(BD¯) [Since BD¯=DC¯]BD¯=102BD¯=5

Now find the length of the median AD¯

Use Pythagorean Theorem to the right angled triangle ADB

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