Question

the base of a prism is triangular in shape with sides 3 cm 4 cm 5 cm find the volume of the prism if its height is 10 cm

Answer 1

$\huge \boxed{ \mathcal{Hello \: Friend }}$

$Base \: Area = \\ \\ \sqrt{s(s - a)(s - b)(s - c)} \\ \\ where \: s = \: semiperimeter \\ \\ again, \: \: s = \frac{a + b + c}{2}$

$By \: putting \: the \: values \: we \: get :- \:$

$s = \frac{3 + 4 + 5}{2} \\ \\ s = \frac{12}{2} \\ \\ \therefore \: s = 6$
$Area = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: = \sqrt{6(6 - 3)(6 - 4)(6 - 5)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: = \sqrt{6 \times 3 \times 2 \times 1} \\ \\ \: \: \: \: \: \: \: \: \: \: \: = \sqrt{36} \\ \\ \: \: \: \: \: \: \: \: \: \: \: = 6 {cm}^{2}$

$Area \: Of \: Triangular \: Prism \\ \\ = Base \: Area \times Height \\ \\ = 6 \times 10 \: {cm}^{2} \\ \\ = 60 \: {cm}^{2}$

$\boxed{Hope \: The \: Above \: Answer \: Helps }$

$\mathbb{PLEASE \: MARK \: BRAINLIEST}$

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Answer 2

Thank you for asking this question, here is your answer:

But the original question had 20cm height so I am solving according to that:

So  first of all we will look at the area

and we know that area of triangle is 1/2 b h

And the area of 3rd angle is 1/2 (3) (4)

The answer of that would be 6cm²

Now we will use this formula:

area of prism is area of base ×height

and that would be

6×20

= 120cm³

So the final answer for this question is 120cm³

If there is any confusion please leave a comment below.