Trapezoid

 

Given an isosceles trapezoid with bases of 8 and 18 and an area of 120 square units, what is the number of units in the length of one of the non-parallel sides?  

 

Area of a trapezoid is the height times half the sum of the top base plus the bottom base. 

 

                                                 A  =  (h) • (b_top + b_bottom) / 2  

 

                                             120  =  (h) • 26 / 2  

 

from this we get                         h  =  120 / 13  =  9.2308   

 

The height dropped from the top left corner intersects the bottom base at 5 from the left.  

The non-parallel side of the trapezoid is the hypotenuse of the right triangle thus formed.  

 

Use Pythagoras Theorem          c²  =  (9.2308)² + (5)²  =  110.207  

 

                                               side  =  sqrt(110.207)  =  10.5   

 

When I was doing this on the calculator, I didn't round the numbers.  

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