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1. What is the perimeter of the trapezoid shown?

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

 

 Nov 30, 2018
 #1
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If we draw a perpendicular from the top right vertex to the lower base......we will create a 30-60-90 right triangle.....the right side of the trapezoid will be the hypotenuse = 2

And the height of this triangle = side opposite the 60” angle = sqrt(3)  =  height of trapezoid

 

The angle opposite the 30 degree angle at the top  = (1/2)hypotenuse = 1

Using symmetry....we have the same situation on the left side of the trapezoid

 

So...the perimeter =    2 units on  the top base.....2 + 1 + 1 = 4 units on the bottom base

And 2(2) = 4 units on the sides

So......the perimeter is   2 + 4 + 2(2) = 10 units 

 

 

Area   =   (1/2) height of trapezoid ( sum of base lengths)  =

 

(1/2)sqrt(3) *  ( 2 + 4)  =

 

(1/2) sqrt (3) (6)  =

 

(3)sqrt (3)    units^2

 

THANKS TO EP FOR POINTING OUT MY ERROR IN THE HEIGHT CALCULATION.....!!!!

 

 

cool cool cool

 Nov 30, 2018
edited by CPhill  Nov 30, 2018

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