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What is the area of the trapezoid shown?

 

Guest Dec 4, 2017
edited by Guest  Dec 4, 2017
edited by Guest  Dec 4, 2017
edited by Guest  Dec 4, 2017

Best Answer 

 #1
avatar+7155 
+2

First let's draw two lines perpendicular to the base, forming two right triangles, like this...

 

 

Now we can find  h  and  x  .

 

sin 60°  =  h / 2          so          h   =   2 sin 60°   =   √3

 

cos 60°  =  x / 2          so          x   =   2 cos 60°   =   1

 

So...

the height of the trapezoid   =   √3   ,

the first base   =   2  ,   and

the second base   =   2 + 1 + 1  =  4

 

area of trapezoid  =  (first base + second base)/2  *  height

area of trapezoid  =  (2 + 4)/2  *  √3

area of trapezoid  =  3√3    sq. units

hectictar  Dec 4, 2017
 #1
avatar+7155 
+2
Best Answer

First let's draw two lines perpendicular to the base, forming two right triangles, like this...

 

 

Now we can find  h  and  x  .

 

sin 60°  =  h / 2          so          h   =   2 sin 60°   =   √3

 

cos 60°  =  x / 2          so          x   =   2 cos 60°   =   1

 

So...

the height of the trapezoid   =   √3   ,

the first base   =   2  ,   and

the second base   =   2 + 1 + 1  =  4

 

area of trapezoid  =  (first base + second base)/2  *  height

area of trapezoid  =  (2 + 4)/2  *  √3

area of trapezoid  =  3√3    sq. units

hectictar  Dec 4, 2017

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