SOLUTION: Using a trapezoid, I need to determine the a) area and b) the perimeter of the figure the top side is 4 in., the left and right sides are 3.2 in., and the bottom side is 9 in

The perimeter is very easy, just add up all the sides of
the trapezoid:

Perimeter = left side + top side + right side + bottom side =

Perimeter = 3.2in + 4in + 3.2in + 9in = 19.4in
  
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Draw perpendiculars (in green) from the upper corners to the 
bottom side, and label their lengths h:



Next we will calculate the three parts of the bottom side
which these two green perpendiculars have divided it into.

Since the top side is 4in the middle part of the bottom 
is 4in also.

The whole bottom side is 9in, so the sum of the left and
right parts is 9 - 4 or 5in.  and since the left part and
the right part are the same length, they are each half
of 5 or 2.5in each 





Next we calculate the length h by using
the Pythagorean theorem:


2.5² + h² = 3.2²
6.25 + h² = 10.24
       h² = 3.99
        h = 1.997498436 in

The area of the right triangle on the left is

A = ½bh
A = ½(2.5)(1.997498436)
A = 2.496873044 in²

That's also the area of the right triangle on
the right.

The area of the rectangle in the middle is

A = lw
A = 4(1.997498436)


So the total area of the trapezoid:

Area of triangle on the left  =  2.496873044 in²
Area of middle rectangle      =  7.989993742 in²
Area of triangle on the right =  2.496873044 in²
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Total area of trapezoid       = 12.983739830 in²

Edwin