What is the surface area of a pyramid that has a height 12 m and the base is a rectangle of dimensions 88 m and 25 m.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The surface area of the pyramid can be calculated by estimating the sum of the triangles that make up the pyramid.

The height of the pyramid is 12. The diagonals of the rectangle meet at a point that is 44 m from the sides with length 25 and 12.5 m from the sides with length 88.

For the triangles formed by the sides that are 88 m in length, the surface area is `(1/2)*88*sqrt(12^2+12.5^2)` . For the triangles formed by the sides that are 25 m in length, the surface area is `(1/2)*25*sqrt(44^2 +12^2)`

The total area of the four triangles isĀ `88*sqrt(300.25)+25*sqrt2080`

If the area of the rectangle at the bottom is included, the surface area of the pyramid is `2200+88*sqrt300.25+25*sqrt2080` = 4865.01

The required surface area of the pyramid is 4865.01 m^2

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