Find the area of the total surface of a rectangular parallelepiped, at the base of which is a square with a side of 4 cm and a height of 6 cm. Find the side of the square if its area is 100 cm 2. A rectangular parallelepiped is made of two identical cubes with an edge of 3 cm. Find the sum of the lengths of the edges of a rectangular parallelepiped.
1) The total surface of the parallelepiped is the total area of the faces. We have 2 equal squares and 4 equal rectangles. Hence, the total surface area is equal to:
S = 2 * a ^ 2 + 4 * a * h = 2 * 16 + 4 * 24 = 32 + 96 = 128 cm².
2) The area of a square is the square of the size of its side, which means:
a = S ^ (1/2) = 100 ^ (1/2) = 10 cm.
3) The cubes were folded and received a parallelepiped, in which the length is twice the length of the cube, the width and height have not changed.
The sum of the lengths of the ribs is the sum of the length, width and height, multiplied by 4:
L = 4 * (3 + 6 + 3) = 48 cm.
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