Find the height of a regular truncated quadrangular pyramid in which the sides = 10cm and 2cm, and the side edge is 9cm.

| January 3, 2021 | education

At the bases of the truncated pyramid are squares with sides of 2 cm and 10 cm.
Let us construct the diagonals A1C1 and AC of the pyramid bases and determine their length.
A1C1 ^ 2 = 2 * 2 ^ 2 = 8.
A1C1 = 2 * √2 cm.
AC ^ 2 = 2 * 10 ^ 2 = 200.
AC = 10 * √2 cm.
The diagonal section of the truncated pyramid is an isosceles trapezoid, in which the bases are 2 * √2, 10 * √2, the sides are 9 cm.
We will construct the height С1Н of the trapezoid, which is the height of the truncated pyramid.
The height С1Н divides the base of the AC into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases of the trapezoid. CH = (A1C1 – AC) / 2 = 8 * √2 / 2 = 4 * √2 cm.
Then in a right-angled triangle CC1H, according to the Pythagorean theorem, C1H ^ 2 = CC1 ^ 2 – CH ^ 2 = 81 – 32 = 49. C1H = 7 cm.
Answer: The height of the truncated pyramid is 7 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.