D1 is a regular prism, the perimeter of the side face is 36, the area of the base is 64. find the area
| September 3, 2021 | education
D1 is a regular prism, the perimeter of the side face is 36, the area of the base is 64. find the area of the lateral surface of the prism
Since the prism is correct, there is a square at its base, then the side of the square will be equal to:
AB = √Savsd = √64 = 8 cm.
The side face of a regular pyramid is a rectangle. By condition, the perimeter of the side face is 36 cm.
P = 2 * (AB + AA1).
36 = 2 * (8 + AA1).
36 = 16 + 2 * AA1.
AA1 = (36 – 16) / 2 = 8 cm.
Let us determine the area of the lateral surface of the prism.
Side = 4 * AB * AA1 = 4 * 8 * 8 = 256 cm2.
Answer: The lateral surface area is 256 cm2.
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