The lateral surface of a regular quadrangular prism is 30 cm2, and the total surface is 48 cm2. Find the height of the prism.
| February 22, 2021 | education
Subtracting the lateral surface area from the total surface area gives the area of two bases.
S floor – S side = 2 * Sb = 48 – 30 = 18 cm2.
Then Sbn = 18/2 = 9 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 = 9.
AB = 3 cm.
Determine the area of the lateral rib. S rib = S side / 4 = 30/4 = 7.5 cm2.
Sedge = AB * AA1.
AB * AA1 = 7.5.
AA1 = 7.5 / 3 = 2.5 cm.
Answer: The height of the prism is 2.5 cm.
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