SOLUTION: I don't understand how to find the area in this question using the information given, the Question asks: The perimeter of a Trapezoid is 29 inches. Its nonparallel sides are 4 inch

Question 197372This question is from textbook Geometry Integration Applications Connections
: I don't understand how to find the area in this question using the information given, the Question asks: The perimeter of a Trapezoid is 29 inches. Its nonparallel sides are 4 inches and 5 inches long. If the height of the trapezoid is 3 inches, find its area. This question is from textbook Geometry Integration Applications Connections

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let's begin with the formula for the perimeter of a general quadrilateral, simply the sum of the measures of the four sides, so:

We know that the perimeter of this trapezoid is 29 and we know the lengths of 2 of the sides, namely the two non-parallel sides which measure 5 and 4 for a total of 9. That means that the sum of the measures of the two parallel sides must be 29 - 9 = 20.

Now, let's look at the formula for the area of a trapezoid -- the average of the measures of the two parallel sides times the height.

But from our analysis above we know that the sum of the measures of the two parallel sides is 20, regardless what their individual measures are, so just divide 20 by 2 and multiply by the height, 3. 10 times 3 is 30 square units.

John

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