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# Area and Perimeter of Quadrilaterals Practice Problems (page 2)

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McGraw-Hill Professional
Updated on Oct 3, 2011

#### SOLUTION 3

The total area of the sign, A total , is equal to the product of the base (or top) length and the height:

A total = 25 meters × 15 meters = 375 meters squared

This is the same total area as that found in Solution 3-5. Thus, 45 percent of this, A top , is the same as in Solution 3-5, that is, 168.75 meters squared. This means that the area of the bottom portion, A bottom, is:

A bottom = A totalA top

= (375 − 168.75) meters squared

= 206.25 meters squared

Let x be the distance, in meters, that the dividing line is to be placed from the bottom edge of the sign. Then x represents the lengths of the two vertical sides of the bottom rectangle. We already know that the dividing line (which is the top edge of the bottom rectangle) is 25 meters long, as is the base. So we get this formula:

A bottom = 25 x

We know that A bottom = 206.25 meters squared. So we can plug this into the above equation and solve for x :

206.25 = 25 x

x = (206.25 meters squared)/(25 meters)

= 8.25 meters

The dividing line should therefore be placed 8.25 meters above the bottom edge of the billboard. Is this placement fair? That will have to be determined by mutual discussions between the lawyers for Top Inc. and Bottom Inc., doubtless at shareholder expense.

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