To find the missing height $h$ of the pyramid, we can use the formula for the volume of a pyramid:

$V = \frac{1}{3} B h$

Where:

• $V$ is the volume of the pyramid,
• $B$ is the area of the base,
• $h$ is the height of the pyramid.

We are given:

• $V = 172 \, \text{cm}^3$,
• $B = 40 \, \text{cm}^2$,
• $h$ is the unknown.

Rearranging the formula to solve for $h$:

$h = \frac{3V}{B}$

Now, substitute the values of $V$ and $B$:

$h = \frac{3 \times 172}{40}$

Let me calculate that.

$h = \frac{516}{40} = 12.9 \, \text{cm}$

So the missing height $h$ is 12.9 cm, and the correct answer is:

a. 12.9 cm

Would you like further details or have any other questions?

Here are 5 related questions for practice:

1. What is the formula for the volume of a rectangular pyramid?
2. If the base area were doubled, how would it affect the height?
3. How do you calculate the surface area of a pyramid?
4. What happens to the volume if the height of the pyramid is halved?
5. If the volume is 300 cm³ and the base area is 50 cm², what is the height?

Tip: When solving for height in a pyramid, always isolate $h$ by multiplying both sides by 3 and dividing by the base area $B$.