The surface area of the composite figure is calculated as:
SA = 622 cm²
How to find the surface area of a composite figure?
The composite figure comprises a rectangular rectangle and a triangular prism, thus, we have to find the surface area of each then subtract the area of the surface where they both meet which is a square.
Surface Area of the rectangular prism = 2(wl + hl + hw), where l is the length, w is the width and h is the height.
SA = 2(12·11 + 7·11 + 7·12)
SA = 586 cm²
Surface Area of the triangular prism = (Perimeter of the base × Length) + (2 × Base Area) = (a + b + c)L + bh
a = 3 cm
b = 4 cm
c = 5 cm
L = 4 cm
b = 4 cm
h = 3 cm
Plug in the values:
SA = (3 + 4 + 5)4 + 4*3
SA = 60 cm²
Area of the surface where they meet = L * W = 3 * 4
= 12 cm²
Surface area of the composite figure = 586 + 60 - 2(12)
SA = 622 cm²