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So I already know how to calculate base area given all 3 edges. I need to use Herom Formula. Now I'm left with finding the height of the prism. What formula should I apply here to find the height of the prism given that I already have surface area of 1620cm (Sqr) and base area of 360cm(sqr) ? Pic of the prism:

enter image description here

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Express the surface area by the height of the prism to have an equation. Note, for example, that the quadrilateral $A_1B_1BA$ is a rectangle (which I assume from the image).

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  • $\begingroup$ Thanks, but I don't know how can I express the surface area by the height of the prism when I don't know what the height of the prism is. Actually I'm pretty bad at math so don't even know how that equation should be solved :( $\endgroup$ – Limpuls Nov 19 '15 at 15:01
  • $\begingroup$ @Limpuls: Let $h$ be the height of the prism. Then, you can have $1620=2\times \text{(the area of the triangle)}+25h+29h+36h$. Then solve this for $h$. $\endgroup$ – mathlove Nov 19 '15 at 15:03
  • $\begingroup$ I found in my book example on how it is being solved and the answer is 10 but I don't get where from does it come. It looks like this: 1620=90H + 2x360 $\endgroup$ – Limpuls Nov 19 '15 at 15:13
  • $\begingroup$ @Limpuls: The equation you wrote is the same as the one I wrote where $H=h$ represents the height of the prism. The 1620 comes from the surface area. The 360 represents the area of the triangle. We have two triangles, so $2\times 360$. $90H$ comes from $25H+29H+36H$ where $25H$ represents the area of the rectangle $A_1B_1BA$ and so on. Note that we have three rectangles $A_1B_1BA, B_1C_1CB$ and $C_1A_1AC$. I hope this helps. $\endgroup$ – mathlove Nov 19 '15 at 15:17
  • $\begingroup$ Yeah it helps, I really appreciate your time I almost got this one, but the answer of 10 is found in the book. I get different answers of equation myself. I think I solve my equation wrong. Do you multiply 2 times 360 get 720 then add 90H and divide by something? $\endgroup$ – Limpuls Nov 19 '15 at 15:26

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