The image shows a triangular pyramid (a tetrahedron) with a triangular base. The given dimensions are:

• The base of the triangle = 9 cm
• The height of the triangle = 2.4 cm

We need to calculate:

1. Volume (V) of the triangular pyramid
2. Surface Area (SA) of the triangular pyramid

Step 1: Calculate the Volume (V)

The volume of a pyramid is given by:

$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$

The base of the pyramid is a triangle, so its area is:

$\text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$

$= \frac{1}{2} \times 9 \times 2.4$

$= \frac{1}{2} \times 21.6 = 10.8 \text{ cm}^2$

Now, using the given height (h), we multiply by the pyramid height and divide by 3:

$V = \frac{1}{3} \times 10.8 \times h$

The height of the pyramid is missing in the diagram. Can you confirm the full height of the pyramid?

Step 2: Calculate Surface Area (SA)

The surface area includes:

1. The base triangle's area.
2. The sum of the areas of the three triangular faces.

To calculate it, we need to know the slant heights of the triangular faces. Do you have more information about the missing height or the slant heights?

Would you like me to estimate the missing height, or do you have more details?

Here are 5 related questions to expand your understanding:

1. How do you find the height of a pyramid if it's missing?
2. What happens to the volume if the height is doubled?
3. How do you calculate the surface area if slant heights are given?
4. What are the real-world applications of calculating pyramid volume?
5. How does the base shape affect the total volume?

Tip:

To fully solve for volume and surface area, ensure all necessary dimensions are available.