The side surface of a regular quadrangular prism is 32 m2 and the total surface is 40 m2. Find the height.
September 1, 2021 | education
| If we subtract the lateral surface area from the total surface area, we get the area of two bases.
S floor – S side = 2 * S main = 40 – 32 = 8 cm2.
Then Sbn = 8/2 = 4 cm2.
Since the prism is correct, then at the base of the prism there is a square, then:
Sosn = a ^ 2, where a is the side of the square.
AB ^ 2 = 4.
AB = 2 cm.
Determine the area of the lateral rib. S rib = S side / 4 = 32/4 = 8 cm2.
Sreb = AB * AA1.
AB * AA1 = 8.
AA1 = 8/2 = 4 cm.
Answer: The height of the prism is 4 cm.
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