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
