In a regular four-pointed prism, the sides are 12 cm and 6 cm: the area
| September 28, 2021 | education
In a regular four-pointed prism, the sides are 12 cm and 6 cm: the area of its lateral surface is half the area of the full surface, calculate the height of the pyramid
Determine the area of the base of the prism.
Sbn = AB * AC = 6 * 12 = 72 cm2.
The total surface area of the prism is:
Sпов = 2 * Sсн + S side. (1)
By condition, Sbok = Sпов / 2, then Sпов = 2 * Sbok.
Substitute in equation 1.
2 * S side = 2 * S main + S side.
Side = 2 * Sb = 2 * 72 = 144 cm2.
Sbok = Ravsd * AA1, where Ravsd is the base perimeter.
144 = 2 * (12 + 6) * AA1.
AA1 = 144/36 = 4 cm.
Answer: The height of the prism is 4 cm.
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