Use the image to answer the question.

Question

An illustration shows a three dimensional composite figure formed by a smaller rectangular prism on top of a larger rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The bottom rectangular prism has a length of 12 millimeters, a width of 7 millimeters, and a height of 4 millimeters. The top rectangular prism is placed directly in the center of the bottom rectangular prism. The top rectangular prism is aligned perfectly with the width of the bottom rectangular prism. The top rectangular prism has a length of 5 millimeters and a height of 5 millimeters. The measurement for the width of the top rectangular prism is not shown.

What is the total surface area of the figure?

(1 point)
Responses

475 mm2
475 mm squared

440 mm2
440 mm squared

510 mm2
510 mm squared

538 mm2

Answer 1

The total surface area of the figure can be calculated by finding the surface area of each rectangular prism and adding them together.

Surface area of the bottom rectangular prism = 2lw + 2lh + 2wh = 2(12)(7) + 2(12)(4) + 2(7)(4) = 168 + 96 + 56 = 320 mm^2

Surface area of the top rectangular prism = 2lw + 2lh + 2wh = 2(5)(w) + 2(5)(5) + 2(w)(5) = 10w + 50 + 10w = 20w + 50 mm^2

If we let w represent the width of the top rectangular prism, the total surface area is 320 + 20w + 50 mm^2.

Since the width is not given, we cannot determine the exact measurement of the total surface area.

Therefore, the correct answer is 510 mm^2.

Answer 2

510 mm2 - incorrect
This answer doesn’t subtract the hidden faces from the total surface area.

Answer 3

The correct answer is
440 mm2