Question

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.

Answer 1

REF.image

Sol:

Vol. of $△$ ular prism =

Area of $△$ ular base $\times$ height.

$\therefore$ Area of triangular base =

area of triangle PQR

By heron's formula.

$S=\sqrt{S(s-a)(s-b)(s-c)}$

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

$\therefore Areaof△PQR=$

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

$S=\sqrt{6(6-3)(6-4)(6-5)}$

$=\sqrt{3\times 2\times 3\times 2\times 1}$

$=6c{m}^2$

$\therefore$ vol. of Prism $=6\times 10$

$=60c{m}^3$Answer.