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What is the area of the trapezoid shown? Express your answer in the simplest exact form.


 

 Apr 22, 2021
 #1
avatar+11852 
+1

What is the area of the trapezoid shown?

 

Hello Guest!

 

\(A=\dfrac{1}{2}(2+2a+2)\cdot h\\ a=2cos60°\\ h=2sin60°\)

\(A=\dfrac{1}{2}(2+2\cdot 2cos60°+2)\cdot 2sin60°\\ \color{blue}A=5.196\)

laugh  !

 Apr 22, 2021
edited by asinus  Apr 23, 2021
 #2
avatar+121002 
+2

Drawing  a perpendicular  from the  top left  vertex  to   the  base  forms a 30-60-90  right triangle

 

The  height   =  sqrt (3)

And  the  base of this triangle  = 1

 

So...by  symmetry......the  bottom  base of the  trapezoid  =  4

 

So...the area    =

 

(1/2) sqrt (3)  (  4 + 2)  =

 

 ( 3 sqrt  3)    units^2   

 

 

cool cool cool

 Apr 23, 2021

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