Find the area of the full surface of a regular quadrangular prism, the side of the bases

| April 10, 2021 | education

Find the area of the full surface of a regular quadrangular prism, the side of the bases of which is 6cm and the diagonal of the side edge is 10cm.

The side of the base, the height of the prism and the diagonal of the side face make up a right-angled triangle (the height of the prism is perpendicular to the base of the prism). The height of the prism and the side of the base are the legs, and the diagonal of the side face is the hypotenuse.

We calculate the height of the prism using the Pythagorean theorem:

10² = 6² + h².

h² = 10² – 6² = 100 – 36 = 64.

h = √64 = 8 (cm).

Let’s calculate the area of ​​the lateral surface of a quadrangular prism (it is 4 equal rectangles with sides equal to the height of the prism and the side of the base).

Side = (8 * 6) * 4 = 192 (cm²).

Let’s calculate the area of ​​the bases (there are two of them in the prism, they are equal squares, since the prism is correct).

Sb = (6 * 6) * 2 = 72 (cm²).

Find the total surface area of ​​the prism:

Sp.p = Sbok + Sbn = 192 + 72 = 264 (cm²).



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