Question

Question
Use the image to answer the question.

An illustration shows the unfolded version of a rectangular prism composed of 6 rectangles. There are four adjoining rectangles positioned horizontally. The first and third are similar and smaller. The second and fourth are similar and bigger. The first rectangle is labeled 1 millimeter on the top horizontally. The fourth rectangle is labeled as 5 millimeters on the bottom and 4.5 millimeters on the right side. The second rectangle shares the top and bottom sides with two similar rectangles, one on each side.

What is the surface area of the rectangular prism?(1 point)
mm2

Answer 1

To find the surface area of the rectangular prism, we need to find the area of each of the six rectangles and then add them all together.

Given:
First rectangle: 1 mm x ? mm
Second rectangle: ? mm x ? mm
Third rectangle: 1 mm x ? mm
Fourth rectangle: 5 mm x 4.5 mm

Let's find the missing sides of the second rectangle: Since the second rectangle shares both the top and bottom sides with two similar rectangles (first and third), the missing sides are 4.5 mm and 1 mm respectively.

Now, calculate the areas of each rectangle:
First rectangle: 1 mm x 1 mm = 1 mm²
Second rectangle: 1 mm x 4.5 mm = 4.5 mm²
Third rectangle: 1 mm x 1 mm = 1 mm²
Fourth rectangle: 5 mm x 4.5 mm = 22.5 mm²
Fifth rectangle (the side of the second rectangle): 1 mm x 4.5 mm = 4.5 mm²
Sixth rectangle (the side of the second rectangle): 1 mm x 4.5 mm = 4.5 mm²

Now, add up the areas of all six rectangles:
1 mm² + 4.5 mm² + 1 mm² + 22.5 mm² + 4.5 mm² + 4.5 mm² = 38 mm²

Therefore, the surface area of the rectangular prism is 38 mm².