Question

the base of prism is tringular in shpe with side 3 cm ,4cm , 5 cm find the volume of of the if its height is 10cm​

Answer 1

Answer:

Answer:–

• The volume of the prism,V=60cm³

Given:–

• The sides of a base are 3cm,4cm and 5cm.
• The height of the prism,h=10cm.

To find:–

• The volume of a prism,v=?

Solution:–

It is given that,

The sides of a base triangle=3cm,4cm and 5cm.

Now,

$Semiperimeter,S = \frac{a + b + c}{2}$

$S = \frac{3 + 4 + 5}{2}$

$S = \frac{12}{2} = 6cm$

So,The Semiperimeter,S=6cm

Area of the triangular base of a prism=$\sqrt{s(s - a)(s - b)(s - c)}$

⇒ $\sqrt{6(6 - 3)(6 - 4)(6 - 5)}$

⇒ $\sqrt{6(6)} = \sqrt{36} = 6 {cm}^{2}$

Now,

Volume of a prism=Area of triangular base×height

⇒ $Volume,V = 6 {cm}^{2} \times 10cm$

⇒ $v = 60 {cm}^{3}$

So,The Volume of a prism is 60cm³.

Answer 2

$\huge\red{\underline{\overline{\mathbb{sᴏʟᴜᴛɪᴏɴ!}}}}$

Given, sides of prism are 3 cm, 4 cm and 5 cm and height =10 cm

Let s be the semi-perimeter of the triangular base of the prism.

Then S = 3+4+5/2

=6 cm

Therefore, the area of the prism :

=> √s(s−a)(s−b)(s−c)

= > √6(6−3)(6−4)(6−5)

= > √6×3×2×1

=> √36

=> 6 cm³

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Sorry Puneeth!