Of course! Let’s break down the problem and solve it step-by-step.
Step 1: Identify the given values.
- The height (h) of the pyramid is 12 feet.
- The length of each side (s) of the square base is 7 feet.
Step 2: Calculate the area of the square base.
Since the base of the pyramid is a square, the area (A) of the base can be found using the formula:
[tex]\[ \text{Area of base} = s^2 \][/tex]
Substituting the value of [tex]\( s = 7 \)[/tex] feet into the formula, we get:
[tex]\[ \text{Area of base} = 7^2 = 49 \, \text{square feet} \][/tex]
Step 3: Use the volume formula for a square pyramid.
The formula for the volume (V) of a square pyramid is given by:
[tex]\[ V = \frac{1}{3} \left( s^2 \times h \right) \][/tex]
We have already determined that [tex]\( s^2 = 49 \)[/tex] square feet and we know that the height [tex]\( h = 12 \)[/tex] feet. Substituting these values into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \left( 49 \times 12 \right) \][/tex]
Step 4: Perform the multiplication inside the parenthesis.
[tex]\[ 49 \times 12 = 588 \][/tex]
Step 5: Multiply by [tex]\(\frac{1}{3}\)[/tex] to find the volume.
[tex]\[ V = \frac{1}{3} \times 588 = \frac{588}{3} = 196 \, \text{cubic feet} \][/tex]
Final Answer:
The volume of the square pyramid is [tex]\( 196 \, \text{cubic feet} \)[/tex] and the area of the base is [tex]\( 49 \, \text{square feet} \)[/tex].
So, we have:
- The base area: [tex]\(49 \, \text{square feet}\)[/tex]
- The volume: [tex]\(196 \, \text{cubic feet}\)[/tex]
