At the base of the rectangular parallelepiped is a rectangle with sides 3cm, 4cm. The height of the parallelepiped is 5 cm.

| June 26, 2021 | education

At the base of the rectangular parallelepiped is a rectangle with sides 3cm, 4cm. The height of the parallelepiped is 5 cm. Find: a) the length of the diagonal of the parallelepiped; b) lateral surface area.

Because at the base of the parallelepiped is a rectangle, then the diagonals of the base are equal and divide the base into right-angled triangles.

Find the diagonal of the base using the Pythagorean theorem:

√ (9 + 16) = √25 = 5 (cm).

Because the parallelepiped is rectangular, the side edges of the parallelepiped are perpendicular to the base.

The triangle formed by the base diagonal, the side edge and the parallelepiped’s diagonal is rectangular.

By the Pythagorean theorem, we find the diagonal of the parallelepiped.

√ (25 + 25) = √50 = √ (25 * 2) = 5√2 (cm).

Let us determine the area of ​​the lateral surface by adding up the areas of all the lateral faces:

3 * 5 + 4 * 5 + 3 * 5 + 4 * 5 = 5 * (3 + 4 + 3 + 4) = 5 * 14 = 70 (sq. Cm).

Answer: the diagonal of the parallelepiped is 5√2 cm, the lateral surface area is 70 sq. Cm.



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