SOLUTION: The base of a prism is a quadrilateral whose sides are 3.5 cm, 4 cm, 5 cm , and 6 cm. Its shorter diagonal is 6 cm.long. If the altitude is 20 cm., find its volume.

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Question 1018062: The base of a prism is a quadrilateral whose sides are 3.5 cm, 4 cm, 5 cm , and 6 cm. Its shorter diagonal is 6 cm.long. If the altitude is 20 cm., find its volume.
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Below is the quadrilateral ABCD which is the base of the prism.
The green line is the shorter diagonal.



The volume of a prism is the area of the base multiplied
by the height, or altitude.

We know the altitude is 20 cm.  We need the area of the
quadrilateral ABCD base.  This quadrilateral's area is the 
sum of the areas of triangles ABC and ACD.

We will use Heron's formula for the area of a triangle:

A%22%22=%22%22sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29, where

s%22%22=%22%22semiperimeter%22%22=%22%22expr%281%2F2%29%28a%2Bb%2Bc%29 

For triangle ABC,  

s%22%22=%22%22expr%281%2F2%29%283.5%2B4%2B6%29%22%22=%22%22expr%281%2F2%29%2813.5%29%22%22=%22%226.75

A%22%22=%22%22sqrt%286.75%286.75-3.5%29%286.75-4%29%286.75-5%29%29%22%22=%22%226.726521668

For triangle ACD,  

s%22%22=%22%22expr%281%2F2%29%286%2B5%2B6%29%22%22=%22%22expr%281%2F2%29%2817%29%22%22=%22%228.5

A%22%22=%22%22sqrt%288.5%288.5-6%29%288.5-5%29%288.5-6%29%29%22%22=%22%2213.63589014

Add the two triangles' areas:

6.726521668 + 13.63589014 = 20.36241182 cm²

Multiply by the given altitude = 20 cm to get the desired volume:

(20.36241182 cm²)(20 cm) = 407.2482362 cm³

Edwin

Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
The base of a prism is a quadrilateral whose sides are 3.5 cm, 4 cm, 5 cm , and 6 cm. Its shorter diagonal is 6 cm.long.
If the altitude is 20 cm., find its volume.
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What if a 6 cm diagonal is the OTHER diagonal?

1) Is it possible?

2) Will the result be the same?

3) Why they refer to 6 cm diagonal as the shorter diagonal?

4) What if the listed sides are not consecutive sides?

I found their formulation strange and unfulfilled and didn't start solve it :)