Question

The base of a prism is triangular in shape with sides 3cm,4cmand5cm.Find the volume of the prism if its height is 10cm.​

Answer 1

777.688cm3

$(\sqrt{12 \times (12 - 3) \times (12 - 4) \times (12 - 5) ) \times 10$

Answer 2

Hello mate..

$\huge \tt\underline{A}\rm\underline{nswer :}$

Given:

• Sides of the prism = 3cm, 4cm and 5cm.
• Height of the prism = 10cm.

$\:$

To Find:

Volume of the prism with the given measurements.

SOLUTION:

$\bold \purple{volume \: of \: triangular \: prism = area \: of \: the \: base \times height}$

Given measurements of the sides are 3,4,5.

$\bold \purple{area = s(s - a)(s - b)(s - c)}$

Where,

$\bold \purple{s = \frac{a + b + c}{2} }$

$\bold{ \frac{3 + 4 + 5}{2} = \frac{12}{2} = 6}$

$\bold{ \implies \sqrt{6(6 - 3)(6 - 4)(6 - 5)} } \\ \bold{ \implies \sqrt{6 \times 3 \times 2 \times 1} } \\ \bold { = 6 {cm}^{2} }$

∴ Volume of the prism = 6×10 = 60 cm³

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{(or)}$

3 cm, 4 cm and 5 cm are the sides of right triangle.

∴Area of the triangle = ½bh

= ½ × 3 × 4 = 6 cm²

∴ Volume of the prism = base area × height

= 6 × 10 = 60 cm³.

HOPE THIS HELPS YOU..