Question

Find the height h of the parallelogram.

A. 12
B. 15
C. 18
D. 21

IMAGE: https://vie1160-912-pps.gradpoint.com/Resource/8766464,0/Assets/testitemimages/geometry_b/area/mc015-1.jpg

Answer 1

I think its either 18 or 15

Answer 2

Do you know the area of a parallelogram ?

Answer 3

yes

Answer 4

What is it?

Answer 5

the area would 180

Answer 6

To calculate the height h of the parallelogram we need to know its base and area.
b = 18
I don't know the area of tis..
Is the area given?

Answer 7

oh, no i had gotten the area by multiplying 18*10 which is the other height and base and it gave my 180. I don't know how to solve for the other height tho which is supposed to be the answer to the question :/

Answer 8

do you by chance know how to solve it to get the other height calculated?

Answer 9

Is any other detail/info given?

Answer 10

nope that is all

Answer 11

see attached for a few hints

Answer 12

thanks for the hints @jim_thompson5910 i'll see how I can use them

Answer 13

still need help trying to solve it all together tho :(

Answer 14

let me know if you're able to find h or not

Answer 15

\[\Large {\color{red}{\text{Area of Triangle}}} = {\color{red}{\frac{x*h}{2}}}\]
\[\Large {\color{blue}{\text{Area of Parallelogram}}} = {\color{blue}{180}}\]
\[\Large \text{Area of Trapezoid} = \frac{h*(b_1+b_2)}{2}\]


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In this case,


\[\Large b_1 = x+12\]
\[\Large b_2 = 12\]

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\[\large \text{Area of Trapezoid} = {\color{red}{\text{Area of Triangle}}}+{\color{blue}{\text{Area of Parallelogram}}}\]
\[\Large \text{Area of Trapezoid} = {\color{red}{\frac{x*h}{2}}}+{\color{blue}{180}}\]
\[\Large \frac{h*(b_1+b_2)}{2} = {\color{red}{\frac{x*h}{2}}}+{\color{blue}{180}}\]
\[\Large \frac{h*(x+12+12)}{2} = \frac{x*h}{2}+180\]
\[\Large \frac{h*(x+24)}{2} = \frac{x*h}{2}+180\]
\[\Large \frac{h*x+24h}{2} = \frac{x*h}{2}+180\]
\[\Large \frac{h*x}{2}+\frac{24h}{2} = \frac{x*h}{2}+180\]
\[\Large \frac{h*x}{2}+12h = \frac{x*h}{2}+180\]
Notice after this point, we subtract the terms h*x/2 from both sides and the terms will go away. Effectively eliminating x all together. Leaving just h behind.
\[\Large \frac{h*x}{2}+12h{\color{green}{-\frac{h*x}{2}}} = \frac{x*h}{2}+180{\color{green}{-\frac{h*x}{2}}}\]
\[\Large 12h = 180\]

so if 12h = 180 then h = ???

Answer 16

h=15!

Answer 17

yes correct

Answer 18

thank you very very much @jim_thompson5910 :) it would've taken me a while to get that, thank you for explaining so well.

Answer 19

no problem