Find the side of the rigging and the height of the right-handed quadrangular prism;

| July 4, 2021 | education

Find the side of the rigging and the height of the right-handed quadrangular prism; its total surface area is 40 cm2 and the side surface is 32 cm2

At the base of a regular quadrangular prism lies a square, and the side faces are rectangles.

The total surface area of the prism is equal to the sum of the lateral surface areas and the two bases:

S full = S side + 2 * S main.

Hence:

Sb = (Sful – S side) / 2 = (40 – 32) / 2 = 8/2 = 4 cm2.

The area of the square is equal to the square of the side, therefore the side of the base of this prism is equal to:

a = √Sbase = √4 = 2 cm.

The area of the lateral surface of the prism is equal to the product of the perimeter of the base and the height of the prism:

S side = P * h = 4 * a * h;

h = Sside / P = 32/8 = 4 cm – the height of this prism.



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