To find the height of a square pyramid given its volume and the length of its base side, we can use the formula for the volume of a pyramid:
Volume = (1/3) × Base Area × Height
For a square pyramid, the base area can be calculated as:
Base Area = side × side = base length × base length
In this case, the base length is 3 feet. Therefore, the base area would be:
Base Area = 3 feet × 3 feet = 9 square feet
Now we put the values into the volume formula. We know the volume is 12 cubic feet, and we calculated the base area to be 9 square feet:
12 = (1/3) × 9 × Height
To isolate the height, we can first multiply both sides by 3:
36 = 9 × Height
Next, we divide both sides by 9:
Height = 36 / 9
Height = 4 feet
Therefore, the height of the square pyramid is 4 feet.