Use the image to answer the question.

Question

An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is in the shape of two rectangular prisms. With the section removed, the figure resembles three steps. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 centimeters at the bottom, a width of 2 centimeters, and a height of 18 centimeters. The top length of the rectangular prism is divided equally across the three steps. Each step has a length of 4 centimeters. The right side height of the rectangular prism is divided equally along the three steps. Each step has a height of 6 centimeters.

What is the total surface area of the figure?

(1 point)
Responses

444 cm2 444 cm squared

480 cm2
480 cm squared

552 cm2
552 cm squared

408 cm2

Answer 1

To find the total surface area of the figure, first calculate the surface area of the rectangular prism without the missing section.

The surface area of a rectangular prism can be found using the formula 2lw + 2lh + 2wh, where l is length, w is width, and h is height.

Surface area of rectangular prism = 2(12)(2) + 2(12)(18) + 2(2)(18)
Surface area of rectangular prism = 24 + 432 + 72
Surface area of rectangular prism = 528 cm2

However, since there are three steps missing in the figure, we need to subtract the surface area of these three steps. Each step has a surface area of 12 + 24 + 12 = 48 cm2. Since there are three steps, the total surface area of the missing sections is 144 cm2.

Total surface area = Surface area of rectangular prism - Surface area of missing sections
Total surface area = 528 - 144
Total surface area = 384 cm2

Therefore, the total surface area of the figure is 384 cm2.