A positive pyramid is a truncated pyramid (the base of a positive pyramid is a regular polygon, the sides are all isosceles triangles, the two bottom sides of a positive pyramid are two similar regular polygons, and the sides are identical isosceles trapezoids), and the formula for the area of a positive pyramid can be obtained by adding the areas of each trapezoid side.

The formula for the side area of the positive edge is: S side =1/2n(a+b)h, where n is the number of sides of the regular polygon, a is the length of the side of the regular polygon, b is the length of the upper base of the isosceles trapezoid, and h is the height of the isosceles trapezoid.

For example, if the side length of the bottom 6-sided shape of a positive prism is 4cm, the upper base length of the isosceles trapezoid is 6cm, and the height is 8cm, then the side area is S side =1/2*6(4+6)*8=240 square centimeters.

The formula for the side area of a positive edge platform can also be expressed as S side = (1/2)(c+c’)h, where c and c’ are the circumferences of the upper and lower base surfaces, respectively, and h is the side height of the positive edge platform (i.e. the height of the isosceles trapezoid). The division by 2 in the formula is because the sides of the positive edge are composed of isosceles trapezoids, so the area formula for isosceles trapezoids must be used to calculate the side area.

Assuming that the upper base perimeter of the positive edge platform is 10cm, the lower base perimeter is 14cm, and the side height is 6cm, then the side area according to the formula is S side = (1/2)(10+14)6 = 72cm^2, so the side area of this positive edge platform is 72 square centimetres.

To summarise:

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Recommended reading: “The side area formula of a pyramid”, “The side area formula of a pyramid”, “The side area formula of a rectangular prism”, “The side area formula of a regular prism”.