In a rectangular parallelepiped, the sides of the bases are 20 and 34 cm. One of the diagonals of the base is 42

| February 16, 2021 | education

In a rectangular parallelepiped, the sides of the bases are 20 and 34 cm. One of the diagonals of the base is 42, and the large diagonal of the parallelepiped is 58. Find the total surface area.

Since a parallelepiped lies at the base, its diagonal divides the base into two equal triangles. By Heron’s theorem, we determine the area of the AСD triangle.

The semi-perimeter of the triangle is: p = (AC + СD + AD) / 2 = 48.

Sac = √48 * (48 – 42) * (48 – 20) * (48 – 34) = √112896 = 336 cm2.

Sb = 2 * Sac = 2 * 336 = 672 cm2.

In a right-angled triangle ACC1, we determine the length of the leg CC1.

CC1^2 = AC1^2 – AC^2 = 3364 – 1764 = 1600.

CC1 = 40 cm.

Let us determine the area of the lateral surface.

Sside = P * CC1 = 2 * (20 + 34) * 40 = 4320 cm2.

Let us determine the total surface area.

Sпов = 2 * Sсн + S side = 2 * 672 + 4320 = 5664 cm2.



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