To find the length of the altitude of the prism, we can follow these steps:
1. The area of one base of the prism is given as 81 cm², and since the base is a square, we can find the length of one side of the square base by taking the square root of the area.
So, √81 = 9 cm. This means each side of the square base is 9 cm.
2. The lateral surface area of the prism is given as 144 cm². For a right prism, the lateral surface area can be calculated using the formula:
Lateral Surface Area = Perimeter of Base * Height
Since the base is a square, the perimeter of the base is 4 times the length of one side.
Perimeter of Base = 4 * 9 = 36 cm
3. Now, we can substitute the given lateral surface area into the formula to find the height (altitude) of the prism:
144 cm² = 36 cm * Height
Height = 144 cm² / 36 cm
Height = 4 cm
Therefore, the length of the altitude of the prism is 4 cm.
