Answer:
1,926 cm²
Step-by-step explanation:
A cube is a three-dimensional geometric shape composed of six congruent square faces, each with an area equal to the square of the cube's side length.
The given figure is made by placing a cube with 12 cm sides on top of another cube with 15 cm sides.
Therefore, the total surface area of the given figure is made up of:
- 5 congruent faces of the 12 cm cube.
- 5 congruent faces of the 15 cm cube.
- One face of the 15 cm cube less one face of the 12 cm cube.
As the area of one face of a cube is the square of its side length, then:
[tex]\textsf{Area of one face of the smaller cube} = 12^2= 144\; \sf cm^2[/tex]
[tex]\textsf{Area of one face of the larger cube} =15^2 = 225 \; \sf cm^2[/tex]
So, the total surface area can be calculated as follows:
[tex]\textsf{Total surface area}=(5 \times 144) + (5 \times 225)+(225-144)\\\\\textsf{Total surface area}=720 + 1125+81\\\\\textsf{Total surface area}=1926\; \sf cm^2[/tex]
Therefore, the total surface area of the given figure is:
[tex]\Large\boxed{\boxed{1926\; \sf cm^2}}[/tex]
