# Find the surface area.

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Find the surface area.​ 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