Question

Use the image to answer the question.

An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is also in the shape of a rectangular prism. The top, right, and front faces of the figure are visible. "The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 13.7 centimeters and a height of 11.5 centimeters. The missing section is removed from the bottom right corner of the rectangular prism. The missing section is a rectangular prism that shares a width of 3 centimeters with the rest of the figure. The missing rectangular prism section has a length of 7.5 centimeters and a height of 7.5 centimeters. The remaining length to the left of the missing section both measures 6.2 centimeters. The remaining height above the missing section measures 4 centimeters.

Solve for the total surface area of the figure.

(1 point)

377.8 cm2


353.8 cm2


53.4 cm2


365.8 cm2

Answer 1

353.8 cm²

Work:
- Full prism SA = 2(LW + LH + WH) = 2(13.7·3 + 13.7·11.5 + 3·11.5) = 466.3 cm².
- Removed corner removes these external areas: bottom 7.5·3 = 22.5, right 7.5·3 = 22.5, front 7.5·7.5 = 56.25, back 7.5·7.5 = 56.25. Total removed = 157.5 cm².
- Two new exposed interior faces (top of notch and inner vertical face): 7.5·3 + 7.5·3 = 45 cm².
- Resulting SA = 466.3 − 157.5 + 45 = 353.8 cm².