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Question

There are four adjoining rectangles of the same height positioned so their vertical sides touch. The first and third rectangles from the left are the same size as each other. The second and fourth rectangles from the left are also the same size as each other but wider than the first and third. The first rectangle is labeled 7 centimeters on the left side and 2 centimeters on the bottom side. The fourth rectangle is labeled 10 centimeters on the bottom side. The second rectangle has identical small rectangles touching its top and bottom sides. The small rectangles are the same width as the second rectangle.

The net of a rectangular prism is shown. What is the surface area of the rectangular prism?

(1 point)
Responses

208 cm.2
208 cm.2

306 cm.2
306 cm.2

138 cm.2
138 cm.2

104 cm.2

Answer 1

To find the surface area of the rectangular prism based on the information provided:

1. Determine the dimensions of each rectangle:

   • The first and third rectangles are both: height = 2 cm, width = 7 cm.
   • The second and fourth rectangles are wider. The second rectangle has a height of 2 cm but its width isn't specified exactly; we can deduce that the width of the second rectangle is equal to the width of the fourth rectangle (which is labeled as 10 cm). Since they are identical in height, let's take their height also as 2 cm.

2. Calculate the dimensions of the prism:

   • Length (L) = width of the second rectangle = 10 cm
   • Width (W) = width of the first rectangle = 7 cm
   • Height (H) = height of either rectangle = 2 cm

3. Surface Area formula: The formula for the surface area (SA) of a rectangular prism is: $$SA=2(LW+LH+WH)$$

   Plugging in the values:

   • Length (L) = 10 cm
   • Width (W) = 7 cm
   • Height (H) = 2 cm

   Calculate each term:

   • $LW=10\times 7=70$ cm²
   • $LH=10\times 2=20$ cm²
   • $WH=7\times 2=14$ cm²

Now, sum these up: $$LW+LH+WH=70+20+14=104\text{ cm²}$$

4. Multiply by 2 for the full surface area: $$SA=2\times 104=208\text{ cm²}$$

Thus, the surface area of the rectangular prism is 208 cm². The correct response is:

208 cm²