The surface area of the composite figure is: 300 cm².
What is the Surface Area of a Triangular Prism?
Surface area of a triangular prism = (P)L + bh, where we have the following:
P = perimeter of the base
L = length of the triangular prism
h = height of the triangular base
b = base of the triangular base
What is the Surface Area of a Rectangular Prism?
Surface area = 2(wl + hl + hw), where:
h = height of prism
w = width of prism
l = length of prism.
The surface area of the composite figure = surface area of triangular prism + surface area of rectangular prism - 2(the area where both figures are joined at).
Surface area of the triangular prism = (5 + 12 + 13)4 + (5)(12)
Surface area of the triangular prism = 180 cm²
Surface area of rectangular prism = 2(wl + hl + hw) = 2·(4·12+3·12+3·4) = 192 cm²
The area where both figures are joined at = (l)(w) = (3)(12) = 36 cm².
The surface area of the composite figure = 180 + 192 - 2(36)
The surface area of the composite figure = 180 + 192 - 72
The surface area of the composite figure = 300 cm².
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