Question

the diagram shows a prism whose cross-section is an equilateral triangle of lengths 10cm. the length of the prism is 20cm​

Answer 1

c = 686.6

Explanation:

A=ah+bh+ch+1/2√﹣a⁴+2(ab)²+2(ac)²﹣b⁴+2(bc)²﹣c⁴

=10·20+10·20+10·20+1/2·√﹣10⁴+2·(10·10)²+2·(10·10)²﹣10⁴+2·(10·10)²﹣10⁴

=686.60254

Answer 2

`686.6 cm^2`

Explanation:

From the volume we can find the surface area of one of the triangle sides, by dividing it by its height. You find out that the surface of the triangle face is
`\frac {866}{20}=43.3 cm^2`. Let's pick two of them since we have two side faces (one close to us in the image, one far away), for a total area of
`86.6 cm^2`. At this point we need to add the area of the rectangular faces, which are three rectangles of length 20 and height 10, for a grand total of
`3*10*20 = 600 cm^2`.

Adding everything together, we get
`600+86.6 = 686.6 cm^2`