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

Answer:

The total surface area is 896 $m^{2}$

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 , $x^{2} = 7^{2} + 24^{2} = 625$

x = 25 m

the area of square base is $14^{2} = 196 m^{2}$

the area of each triangular side is $(\frac{1}{2})(base)(height) = (\frac{1}{2})(14)(25) = 135 m^{2}$

such are 4 triangles, thus $(4)(135) = 700 m^{2}$

Thus the total surface area is 196 + 700 = 896 $m^{2}$