Answer:
1134
Explanation:
Since the three cubes are the same size, the area of each square face of the cubes is 3 cm × 3 cm = 9 sq cm.
Since the cubes are attached to the top of the rectangular prism, some faces are not exposed. So, the non-exposed faces are not included when calculating the surface area.
Each cube has 5 square faces exposed, and the rectangular prism has 2 square faces and 4 rectangular faces exposed, minus parts of the top rectangle.
First, calculate the surface area of the three cubes.
SAcubes = 3[5 faces]
= 3[5(9 sq cm)]
= 3[45 sq cm]
= 135 sq cm
Next, calculate the surface area of the rectangular prism.
SArect = 2 square faces + 4 rectangular faces - 3 parts
= 2(9 cm)(9 cm) + 4(9 cm)(24 cm) - 3(9 sq cm)
= 162 sq cm + 864 sq cm - 27 sq cm
= 999 sq cm
Finally, calculate the total surface area of the figure.
SAtotal = cubes + rectangular prism
= 135 sq cm + 999 sq cm
= 1,134 sq cm
Therefore, the surface area of the figure is 1,134 square centimeters.