The smaller sign has dimensions that are 11/44 = 1/4 those of the larger banner, so its perimeter is
... (1/4)×156 inches = 39 inches . . . perimeter
and its area is
... (1/4)²×(1496 in²) = 93.5 in² . . . . . . area
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The linear dimensions of similar figures all have the same scale factor. Those include length, width, perimeter, diameter, radius, height, or any other linear dimension.
The area dimensions of similar figures have a scale factor that is the square of the linear dimension scale factor. (Area is the product of two linear dimensions, each of which has the linear dimension scale factor.)
