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

donkey Apr 19, 2019

#1**+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

CPhill Apr 19, 2019

#2**+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...

Guest Apr 19, 2019

#3**0 **

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

Hypotenuisance Apr 20, 2019