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The two quadrilaterals below have the same area. What is the height of the orange trapezoid?


 Apr 19, 2019
 #1
avatar+106539 
+1

Area of quadrilateral  =  6 * 5  = 30

 

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

 

30 = (1/2) h ( 3 + 7)

 

30  = (1/2) h (10)

 

30  =  5h    divide both sides by  5

 

6  =  h

 

 

cool cool cool

 Apr 19, 2019
 #2
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+1

The purple figure is a para\(\)llelogram, with an area of 5*6=30, since base*height=area...

 

The next figure is a trapezoid...and it's area is  \(\frac{1}{2}{10}{h}=30\), and 5h=30, h=6.

 

 

 

-From Sneaky, maybe CPhill can guess who I am...

 Apr 19, 2019
 #3
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To figure this out, we need to figure out the area of the pink parellelogram.

 

Evaluate 6*5 to get 30 square (units).

 

*The area of a trapezoid is ((a+b)/2)*h.

 

* =  When I say a and b, those are the 3 and 7 side lengths.

 

Now, we can say the area is 5*h, or 5h. 

 

Because the area of the parallelogram is 30 and the area is the same for both shapes, 5h must equal 30.

 

Therefore, h or height is 6.

 

~~Hypotenuisance

 Apr 20, 2019
 #4
avatar+64 
+2

thanks, everyone!

 Apr 20, 2019
 #5
avatar+128 
-2

You're welcome, Donkey!!!

 

~~Hypotenuisance

Hypotenuisance  Apr 21, 2019

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