   Chapter 8.4, Problem 47E 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

Given that the length of each side of a rhombus is 8 cm and that an interior angle measures 60°. Find the exact area of the inscribed circle. To determine

To Find:

The area of the circle inscribed in a rhombus.

Explanation

The side length of the rhombus is 8 cm.

The angle of the rhombus is 60°.

The diagonals of the rhombus AC and BD bisect each other with right angles at the center of the circle.

The diagonals divide the rhombus in to four 30-60-90 triangles.

In the triangle AOB, We know AB = 8.

In 30-60-90 triangles, the side length ratio is 1:2:3.

Therefore, the length of OB = 4 and OA is 43.

Now, draw a perpendicular OP (radius of the circle) to the side AB of rhombus.

It forms a new 30-60-90 right angle triangle AOP.

Now, we know one side OA is 43

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