Use the image to answer the 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)
138 cm.2
138 cm.2
306 cm.2
306 cm.2
104 cm.2
104 cm.2
208 cm.2
208 cm^2
To find the surface area of the rectangular prism, first calculate the area of the four surrounding rectangles.
1st rectangle: (7 cm x 2 cm) x 2 = 28 cm^2
3rd rectangle: same as the 1st = 28 cm^2
2nd rectangle: (7 cm x 10 cm) = 70 cm^2
4th rectangle: (10 cm x 2 cm) = 20 cm^2
Adding all four rectangles: 28 cm^2 + 28 cm^2 + 70 cm^2 + 20 cm^2 = 146 cm^2
Now, calculate the area of the two large rectangles on the sides of the net. One side of the larger rectangle is 7 cm x 10 cm = 70 cm^2. Since there are two sides like this: 70 cm^2 x 2 = 140 cm^2
Adding the area of all the rectangles together: 146 cm^2 + 140 cm^2 = 286 cm^2
Therefore, the surface area of the rectangular prism is 286 cm^2.