The rectangle with sides 24 cm and 10 cm is folded for the first time in the form of a lateral surface of a regular

| September 3, 2021 | education

The rectangle with sides 24 cm and 10 cm is folded for the first time in the form of a lateral surface of a regular quadrangular prism 10 cm high, and in the second – a regular triangular prism with the same height. Compare the areas of the full surfaces of these prisms.

Since in the first case a regular quadrangle is formed at the base, the length of its side will be: 24/4 = 6 cm.

Sb = 6 * 6 = 36 cm2.

Side = 24 * 10 = 240 cm2.

Then the area of the common surface is equal to:

S = 2 * Sb + S side = 2 * 36 + 240 = 312 cm2.

Since in the first case a regular triangle is formed at the base, the length of its side will be: 24/3 = 8 cm.

Sb = (√3 / 4) * 8 ^ 2 = 16 * √3 cm2.

Side = 24 * 10 = 240 cm2.

Then the area of the common surface is equal to:

S = 2 * Sb + S side = 2 * (16 * √3) + 240 = 295.4 cm2.

Answer: The total area of the first prism is greater than the second.



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