The sides of the base of a regular triangular truncated pyramid are 33 cm and 11 cm. Find the height of the pyramid

| August 2, 2021 | education

The sides of the base of a regular triangular truncated pyramid are 33 cm and 11 cm. Find the height of the pyramid if the side face with the base forms an angle of 60 degrees.

Let’s draw the heights BH and B1H1 of equilateral triangles at the base of the pyramid and determine their lengths.

h = a * √3 / 2, where a is the side of the triangle.

BH = 33 * √3 / 2 cm.

B1H1 = 11 * √3 / 2 cm.

The intersection point of the heights O and O1 divides the height in a ratio of 2/1.

Then OH = BH / 3 = (33 * √3 / 2) / 3 = 11 * √3 / 2 cm.

O1H1 = B1H1 / 3 = (11 * √3 / 2) / 3 = 11 * √3 / 6 cm.

Then the segment НР = ОН – О1Н1 = 11 * √3 / 2 – 11 * √3 / 6 = 11 * √3 / 3 cm.

From the right-angled triangle НН1Р we find the height РН1.

НН1 = НР * tg60 = (11 * √3 / 3) * √3 = 11 cm.

Answer: The height of the pyramid is 11 cm.



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