# In a regular truncated pyramid, the perimeters of the upper and lower bases are 4 cm and 10 cm,

In a regular truncated pyramid, the perimeters of the upper and lower bases are 4 cm and 10 cm, respectively, and the apoferm is 20 cm. Determine the lateral surface area

Since the condition does not indicate a regular polygon at the base, then let it be n – a gon.

The side face of a truncated polygon is an isosceles pyramid, then:

S side = (a + b) * h * n / 2, where

a and to the sides of the polygon, h is the height of the trapezoid (apothem of the pyramid), n is the number of faces.

Sside = (a + b) * h * n / 2 = (a * n + b * n) * h / 2.

a * n is the perimeter of one base, b * n is the perimeter of the other base, then:

Sside = (p1 + p2) * h / 2 = (4 + 10) * 20/2 = 140 cm2.

Answer: The lateral surface area is 140 cm2.

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