The base of rectangular parallelepiped abcda1b1c1d1 is a square. The length of the diagonal

| June 9, 2021 | education

The base of rectangular parallelepiped abcda1b1c1d1 is a square. The length of the diagonal of the parallelepiped is AC1 = 15 cm, and the length of the diagonal of its base is AC = 12 cm. Find the area of the lateral surface of the parallelepiped.

Since there is a square at the base of the parallelepiped, in the right-angled triangle ABD the leg AB = BC, then by the Pythagorean theorem, AC ^ 2 = 2 * AB ^ 2.

144 = 2 * AB ^ 2.

AB = 6 * √2 cm.

In a right-angled triangle AA1C, according to the Pythagorean theorem, we determine the length of the leg AA1, which is the height of the parallelepiped.

AA1 ^ 2 = CA1 ^ 2 – AC ^ 2 = 225 – 144 = 81.

AA1 = 9 cm.

Let’s define the perimeter of the square ABCD.

P = 4 * AB = 4 * 6 * √2 = 24 * √2 cm.

Determine the area of the lateral surface of the parallelepiped.

Sside = P * AA1 = 24 * √2 * 9 = 216 * √2 cm2.

Answer: The lateral surface area is 216 * √2 cm2



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