Question

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

Answer 1

The base of a prism is triangular in shape with sides 3 cm, 4 cm and 5 cm. Find the volume of the prism if its height is 10 cm.

Given,

Sides of prism = 3 cm, 4 cm and 5 cm

Height = 10 cm

Now,

$\mathtt{s = \frac{3 + 4 + 5 }{2} = \frac{12}{2} = 6 \: cm } \\ \\ \\ \mathtt{area = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ \\ \mathtt{ = \sqrt{6(6 -3)(s - 4)(s - 5) } } \\ \\ \\ \mathtt{ = \sqrt{6 \times 3 \times 2 \times 1} } \\ \\ \\ \mathtt{ = \sqrt{36} } \\ \\ \\ \mathtt{ = 6 \: cm {}^{2} } \\ \\ \\ \\ \bf{volume = area \: o f \: base \times height} \\ \\ \\ \mathtt{ = 6 \times 10} \\ \\ \\ \mathtt{ = 60 \: cm {}^{3} \: ans}$