The height of a regular truncated quadrangular pyramid is 2 root of 2 cm

| February 12, 2021 | education

The height of a regular truncated quadrangular pyramid is 2 root of 2 cm, and the sides of the base are 1 cm and 4 cm. Find the area of the diagonal section.

Since the pyramid is correct, the upper and lower bases of it are squares, catfish with sides of 1 cm and 4 cm.

From the right-angled triangle of the AСD, according to the Pythagorean theorem, we define the hypotenuse of the AС.

AC ^ 2 = AD ^ 2 + СD ^ 2 = 2 * AD ^ 2 = 2 * 4 ^ 2 = √32.

AC = 4 * √2 cm.

From the right-angled triangle A1C1D1, according to the Pythagorean theorem, we define the hypotenuse A1C1.

A1C1 ^ 2 = A1D1 ^ 2 + C1D1 ^ 2 = 2 * A1D1 ^ 2 = 2 * 12 = 2.

AC = √2 cm.

The diagonal section of the truncated pyramid is an isosceles trapezoid with bases 4 * √2 cm and √2 cm, and a height of 2 * √2 cm.

Determine the area of ​​the trapezoid.

S = (AC + A1C1) * OO1 / 2 = (4 * √2 + √2) * 2 * √2 / 2 = 10 cm2.

Answer: The area of ​​the diagonal section is 10 cm2.



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