Question

A square pyramid has base edge length 14 m. The height of the pyramid is 24 m. Find the surface area of the square pyramid. Use pencil and paper. Draw a net for the figure and find the surface area.

Answer 1

The total surface area is 896
`m^(2)`

Explanation:

The square pyramid is a solid with square base and symmetric 4 triangular faces.

Given that the square base is 14 m and height is 24 m.

The apex of pyramid, center of square and center of any edge of square make a right angled triangle.

Let that height if triangular face be "x".

by pythagoras theorm ,
`x^(2) = 7^(2) + 24^(2) = 625`

x = 25 m

the area of square base is
`14^(2) = 196 m^(2)`

the area of each triangular side is
`((1)/(2))(base)(height) = ((1)/(2))</em></strong><strong>(14)(25) = 135 m^(2)`

such are 4 triangles, thus
`(4)(135) = 700 m^(2)`

Thus the total surface area is 196 + 700 = 896
`m^(2)`