Question

The prism shown has a volume of 35 cm'.
Work out h, the height of the triangular cross section.
h
7 cm
4 cm​

Answer 1

That is an answer......

Answer 2

The height of the triangular cross section of the prism will be $2.5 \ cm$ .

What is prism ?

Prism is a polyhedron comprising an $n-$sided polygon base, a second base which is a translated copy of the first, and $n$ other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases.

And,

Volume of prism $= Base\ Area\ *\ Length$

We have,

Volume of prism $=35 cm^3$

Length of prism $=7cm$

Height of prism $=h\ cm$

We also have,

Base of triangle $=4\ cm$

One of the side of triangle $=5\ cm$

As we have Triangular prism so Base area of prism will be the area of triangle.

so,

Area of triangle $=\frac{1}{2}*base*Height$

                          $=\frac{1}{2} * 4*h$

Area of triangle $=2h$

Now,

Volume of prism $= Base\ Area\ *\ Length$

                       $35=2h*7$

                        $h=\frac{5}{2}$

                         $h=2.5 \ cm$

So, the height of prism is $2.5\ cm$ .

Hence, we can say that the height of the triangular cross section of the prism will be $2.5 \ cm$ .

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