The two edges of a rectangular parallelepiped extending from one vertex are 42 and 24.

| May 2, 2021 | education

The two edges of a rectangular parallelepiped extending from one vertex are 42 and 24. The diagonal of the parallelepiped is 58. Find the surface area of the parallelepiped.

Let’s construct a diagonal AC at the base of the parallelepiped.

Triangle ACD is rectangular, in which, according to the Pythagorean theorem, we define the length of the hypotenuse AC.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 1764 + 576 = 2340.

The AC1 diagonal forms a right-angled triangle ACC1, in which we apply the Pythagorean theorem and determine the length of the CC1 leg.

CC1 ^ 2 = AC1 ^ 2 – AC ^ 2 = 3364 – 2340 = 1024.

CC1 = 32 cm.

Determine the perimeter of the parallelepiped’s base.

Ravsd = 2 * (AB + AD) = 2 * (24 + 42) = 132 cm.

Then the lateral surface area is equal to:

Sside = Ravsd * CC1 = 132 * 32 = 4224 cm2.

Sbn = AB * AD = 24 * 42 = 1008 cm2.

Then Sпов = 2 * Sсн + S side = 2016 + 4224 = 6240 cm2.

Answer: The area of ​​a parallelepiped is 6240 cm2.



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