The height of a regular rectangular truncated pyramid is 4 cm, the sides of the bases are 2 cm
| June 10, 2021 | education
The height of a regular rectangular truncated pyramid is 4 cm, the sides of the bases are 2 cm and 8 cm. Find the area of the diagonal section.
Since, by condition, the pyramid is regular, there are squares at its base and cross-section.
Knowing the sides of the squares, we determine their diagonals.
D = a * √2, where a is the side of the square.
AC = AD * √2 = 8 * √2 cm.
A1C1 = A1D1 * √2 = 2 * √2 cm.
The diagonal section of the truncated pyramid is the isosceles trapezoid АА1С1С.
The area of the trapezoid is:
S = (A1C1 + AC) * OO1 / 2 = (2 * √2 + 8 * √2) * 4/2 = 20 * √2 cm2.
Answer: The area of the diagonal section is 20 * √2 cm2.
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