   Chapter 8.2, Problem 47E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Prove that the area of a trapezoid whose altitude has length h and whose median has length m is A = h m .

To determine

To Prove:

Area of a trapezoid whose altitude has length h and whose median has length m is A=hm.

Explanation

Proof:

Let’s consider a trapezoid ABCD with bases AD=b1 and BC=b2 and altitudes AE and DF measures h units.

Let’s draw the median GH in the trapezoid.

Median of a trapezoid is a segment that joins the midpoints (G and H are the mid points of the line segments AB and CD) of the non-parallel sides.

The median of any trapezoid has two properties:

i. It is parallel to both bases.

ii. Its length equals half the sum of the base lengths.

That is, Median m=12(b1+b2),…(1)

where b1 and b2 are the bases of the trapezoid ABCD

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