The total surface area of a rectangular parallelepiped, at the base of which a rectangle with sides 9

| September 21, 2021 | education

The total surface area of a rectangular parallelepiped, at the base of which a rectangle with sides 9 and 6 cm, is 408 cm2. Find the diagonal of the box.

Spol = 408 cm ^ 2.

a = 9 cm.

b = 6 cm.

d -?

The diagonal of a rectangular parallelepiped d is determined by the formula: d = √ (a ^ 2 + b ^ 2 + h ^ 2), where a, b are the sides of the rectangle that lies at the base, h is the height of the parallelepiped.
The total surface area of ​​a rectangular parallelepiped S floor is determined by the formula: S floor = 2 * S main + 2 * S side + 2 * S tor, where S main is the base area, S late is the lateral surface area, S tor is the area of ​​end surfaces.
Sb = a * b, Sbok = b * h, Stor = a * h.
The formula for the area of ​​the full surface of a rectangular parallelepiped will be: Spol = 2 * a * b + 2 * b * h + 2 * a * h.
Let us express and find the height h.
h = (Spol – 2 * a * b) / (2 * b + 2 * a).

h = (408 cm ^ 2 – 2 * 9 cm * 6 cm) / (2 * 9 cm + 2 * 6 cm) = 10 cm.

6. Find the diagonal of a rectangular parallelepiped: d = √ ((9 cm) ^ 2 + (6 cm) ^ 2 + (10 cm) ^ 2) = 14.7 cm.

Answer: d = 14.7 cm.



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