Question

I got the answer just need to check up with someone

Answer 1

Solution:

Concept:

The volume of the triangular pyramid will be calculated using the formula below

$\begin{gathered} V=\frac{1}{3}\times base\text{ area}\times height \\ \text{Height of the pyramid=H=15yd} \end{gathered}$

In this case, the base is a triangle...Therefore, the area of the base will be calculated using the formula below

$\begin{gathered} \text{Baes area=}\frac{1}{2}\times base\times height \\ \text{base of the triangle=b=5yd} \\ \text{height of triangle=h=12yd} \end{gathered}$

Step 1:

Calculate the area of the base using the formula above

$\begin{gathered} \text{Baes area=}\frac{1}{2}\times base\times height \\ \end{gathered}$

By substituting the values, we will have

$\begin{gathered} \text{Base area=}\frac{1}{2}\times base\times height \\ \text{Base area}=\frac{1}{2}\times5yd\times12yd \\ \text{Base area}=\frac{60yd^2}{2} \\ \text{Base area}=30yd^2 \end{gathered}$

Step 2:

Calculate the volume of the triangular based pyramid using the formula below

$\begin{gathered} V=\frac{1}{3}\times base\text{ area}\times height \\ \text{Where,} \\ \text{Base area=30yd}^2 \\ \text{Height}=H=15yd \end{gathered}$

By substituting the values, we will have

$\begin{gathered} V=\frac{1}{3}\times base\text{ area}\times height \\ V=\frac{1}{3}\times30yd^2\times15yd \\ V=\frac{450yd^3}{3} \\ V=150yd^3 \end{gathered}$

Hence,

The volume of the triangular based pyramid is = 150 yd³