The surface area of the small staircase which is made such that the horizontal piece of each step 10 inches long and 25 inches wide is 1125 in².
What is surface area?
Surface area of any solid or the 3 dimensional body is the area of each faces by which the solid body is enclosed. Surface area of a cuboid is the sum of total area of each face.
The image of the staircase is shown below. This small staircase is made so that the horizontal piece of each step 10 inches long and 25 inches wide.
Thus, the surface area of the trade of stair case is,
[tex]A_{t}=10\times25\\A_{t}=250\rm\;in^2[/tex]
Each step is 5 inches above the previous one. Thus, the surface area of the riser of stair case is,
[tex]A_{r}=25\times5\\A_{r}=125\rm\;in^2[/tex]
Total surface area of one step is,
[tex]A_{s}=3(A_{t}+A_{r})A_{s}=3(250+125)\\A_{s}=3(375)\\A_{s}=1125\rm\;in^2[/tex]
Hence, the surface area of the small staircase which is made such that the horizontal piece of each step 10 inches long and 25 inches wide is 1125 in².
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