   Chapter 8.2, Problem 53E 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

The shaded region is that of a trapezoid. Determine the height of the trapezoid.4 To determine

To Find:

The height of the trapezoid provided as shaded region.

Explanation

Formula Used:

1. Pythagorean theorem for the right angle triangle ABC for the hypotenuse AC,

AC2=AB2+BC2.

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

3. The area A of a trapezoid whose bases have lengths b1 and b2 and whose altitude has length h is given by A=12h(b1+b2)

Calculation:

It is given that the provided diagram has side lengths 6 and 8 units with A and B be the mid points of those sides.

Let the corner point of the triangle be O and the line CD is another base. Since A and B are the mid points of the sides of the triangle, OA=AC=3 and OB=BD=4.

Consider OAB,

Applying Pythagorean Theorem,

AB2=OA2+OB2

AB2=32+42

AB=5 units.

Consider OCD,

Applying Pythagorean Theorem,

CD2=OC2+OD2

CD2=62+82

CD=10 units

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