A building in the shape of a square pyramid is covered with solar panels. The building has a slant height of $12$ feet and a base with side lengths of $15$ feet. The solar panels cost $$ 70$ per square foot to install. How much does it cost to install enough solar panels to cover the entire surface of the building?

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Solution

Step 1: Find the surface area of the pyramid
Surface area of pyramid = Area of base + area of lateral surfaces
Surface area of pyramid $= A r e a o f b a s e + 4 \times a r e a o f t r i a n g l e s$
$= (15 \times 15 + 4 \times \frac{1}{2} \times 12 \times 15) f t^{2} = (225 + 360) f t^{2} = 585 f t^{2}$
Step 2: Find the total cost of covering entire surface
Cost of solar panel $= $ 70 / f t^{2}$
Total cost for covering the entire surface with solar panel $= 585 \times $ 70$ $= $ 40950$
Hence, the total cost for covering the entire surface with solar panel is $$ 40950$ .

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