Answer:
The total surface area is 896 [tex]m^{2}[/tex]
Step-by-step 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 , [tex]x^{2} = 7^{2} + 24^{2} = 625[/tex]
x = 25 m
the area of square base is [tex]14^{2} = 196 m^{2}[/tex]
the area of each triangular side is [tex](\frac{1}{2})(base)(height) = (\frac{1}{2})(14)(25) = 135 m^{2}[/tex]
such are 4 triangles, thus [tex](4)(135) = 700 m^{2}[/tex]
Thus the total surface area is 196 + 700 = 896 [tex]m^{2}[/tex]
