Question

the triangular prism with sides 5 cm, 12 cm and 13 cm and its height is 6 cm, find the volume of triangular prism

Answer 1

volume of the triangle =b×h
B means that the base of the prism.
to find the base use heron's formula.
and multiple with hight.

s=A+B+C/2
s=5+12+13/2=15

A=root over 15 (15-5)(15-12)(15-13) = 30

V=b×h
V=30×6
V=180

Answer 2

Answer:

180 cubic cm.

Step-by-step explanation:

We are given that the triangular prism with sides 5 cm, 12 cm and 13 cm and its height is 6 cm.

a = 5

b = 12

c = 13

h = 6

Formula : $V=\frac{1}{4}h\sqrt{-a^4+2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4$

Substitute the values in the formula

$V=\frac{1}{4}(6)\sqrt{-5^4+2(5 \times 12)^2+2(5 \times 13)^2-12^4+2(12 \times 13)^2-13^4}$

$V=\frac{1}{4}(6)(120)$

$V=180 cm^3$

Hence the volume of triangular prism is 180 cubic cm.