Question

in the figure shown below, a rectangular pyramid is attached to a rectangular prism.
ab = ef = 4 centimeters, af = eb = 3 centimeters, he = da = 6 centimeters. the slant height of △ekb is 3 centimeters, and the slant height of △hek is 4 centimeters.
what is the surface area of this figure, not including the base?
108 cm²
132 cm²
180 cm²
156 cm²

Explanation:

Step1: Calculate the area of the rectangular prism's lateral faces

The lateral faces of the rectangular prism:

• Two faces with dimensions \(4\times6\): Area \(= 2\times(4\times6)=48\)
• Two faces with dimensions \(3\times6\): Area \(=2\times(3\times6) = 36\)

Step2: Calculate the area of the pyramid's lateral faces

The lateral faces of the pyramid:

• Two triangular faces with base \(4\) and slant height \(3\): Area \(=2\times(\frac{1}{2}\times4\times3)=12\)
• Two triangular faces with base \(3\) and slant height \(4\): Area \(=2\times(\frac{1}{2}\times3\times4)=12\)

Step3: Sum up all the areas

Total surface area (not including the base) \(=48 + 36+12 + 12=108\)

Answer:

\(108\ cm^{2}\) (the first option)