The lateral edge of a straight parallelepiped is 33 cm, the base area is 266 cm2, and the total surface area is 3304 cm2. Calculate the perimeter of the base.
In this task, a rectangular parallelepiped with base measurements of length a, width b and side edge (or height) h = 33 cm is considered.
Since the area of the base Sb = a * b (rectangle) is equal to 266 cm2, we have a * b = 266.
The total surface area Sп = 2 * (a * b + a * h + * h) of a straight parallelepiped is 3304 cm2, which means 2 * (a * b + a * h + b * h) = 3304 or 266 + 33 * (a + b) = 1652, whence a + b = (1652 – 266) / 33 = 1386/33 = 42.
Knowing a + b = 42 cm, it is now easy to calculate the perimeter P of the base of a straight parallelepiped using the formula P = 2 * (a + b).
We have P = 2 * 42 cm = 84 cm.
Answer: 84 cm.
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