Find the surface area.

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Find the surface area.​

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Answer:

Step-by-step explanation:

1. solve for the Area of the base (rectangle) =

             A₁ = lw = (12)(6) = 72 ft²

2. Solve for the “slant height” of the small triangle (base 6)

            a= 12/2 = 6ft

            b= 15

Pythagorean Theorem:  

            C² = a² + b²

            C² = 6² + 15²

            C = √261 = 16. 15549 ft

            h= C ( slant height of triangle base 6)

   so:

           A = (1/2)bh                    (h = slant height not h of the pyramid)

           A₂ = (1/2)bh=(1/2)(6)(16. 15549) = 48.46647 ft²  (side small triangle)

           A₃ = (1/2)bh=(1/2)(6)(16. 15549) = 48.46647 ft²  (small opposite side)

           A₄ = A₂ + A₃ = 96.93294 ft²

      or directly get the areas of 2 triangles:

       A₄ = (1/2)bh × 2 = bh    

       A₄ =  (6)(16.15549) = 96.93294 ft²

3. Solve for the “slant height” of the big triangle (base 12)

            a= 6/2 = 3ft

            b= 15

Pythagorean Theorem:  

            C² = a² + b²

            C² = 3² + 15²

            C = √234 = 15.297 ft

            h= C ( slant height of triangle base 12)

   so:

         areas of 2 triangles:

       A₅ = (1/2)bh × 2 = bh    

       A₅ =  (12)(15.297) = 183.564 ft²

surface Area of the pyramid:

       A = A₁ + A₄ + A₅

        A =  72 +  96.93294  + 183.564 = 352.497 ft²


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