Answer:
120 cm³
Step-by-step explanation:
First we have to find out area of the base
[tex]s = \frac{a + b + c}{2} [/tex]
[tex] = \frac{5 + 12 + 13}{2} [/tex]
[tex] = \frac{30}{2} [/tex]
[tex] = 15[/tex]
Area of base = [tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex] = \sqrt{15(15 - 5)(15 - 12)(15 - 13)} [/tex]
[tex] = \sqrt{15 \times 10 \times 3 \times 2} [/tex]
[tex] = \sqrt{5 \times 3 \times 5 \times 2 \times 3 \times 2} [/tex]
[tex] = 2 \times 3 \times 5[/tex]
[tex] = 30 \: {cm}^{2} [/tex]
Now, let's find the volume of triangular pyramid
[tex] = \frac{1}{3} \times a \times h[/tex]
[tex] = \frac{1}{3} \times 30 \times 12[/tex]
[tex] = 120 \: [/tex] cm³
Hope this helps..
best regards!!
