   Chapter 8.2, Problem 43E 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

Although not all kites are cyclic, one with sides of lengths 5 in., 1 ft, 1 ft, and 5 in. would be cyclic. Find the area of this kite. Give the resulting area in square inches.

To determine

To Find:

The area of the cyclic kite provided.

Explanation

Formula Used:

Definition: A right kite is a kite that can be inscribed in a circle. hat is, it is a kite with a circumcircle (a cycle kite). Thus the right kite is a convex quadrilateral and has two opposite right angles. If there are exactly two right angles, each must be between sides of different lengths. All right kites are bicentric quadrilaterals (quadrilateral with both a circumcircle and an incircle), since all kites have an incircle. One of the diagonals (the one that is a line of symmetry) divides the right kite into two right triangles and is also a diameter of the circumcircle.

Area of the right triangle is 12bh, where b is the base and h is the height of the triangle.

Calculation:

It is given that the lengths of the cyclic kite are 5 in., 1 ft., 1 ft., and 5 in.

Conversion: 1feet = 12 inches.

Therefore the side lengths are 5 in., 12 in., 12 in., and 5 in.

By the definition of cyclic kite, it could be easily predicted that ABC and ADC are two opposite right triangle and with equal base and height

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