The base side of a regular quadrangular prism is 6cm, and its volume is 432cm. Calculate the lateral and full surface areas of the prism.
Since the quadrangular prism is regular, there is a square at its base.
Determine the area of the base of the prism.
Sbn = АD ^ 2 = 6 ^ 2 = 36 cm2.
The volume of the prism is: V = Sbn * AA1, then AA1 = V / Sbn = 432/36 = 12 cm.
Let us determine the area of the lateral surface of the prism.
Sside = Ravsd * AA1 = 4 * AD * AA1 = 4 * 6 * 12 = 288 cm2.
Then Sпов = Sbok + 2 * Sсн = 288 + 2 * 36 = 360 cm2.
Answer: The lateral surface area is 288 cm2, the total surface area is 360 cm2.
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