What is the surface of the rectangular prism?
Slant heights are: 16.6 cm, and 17.2 cm.
The lenghth and width are 20 cm, and 18 cm. They form right triangle with the slant height.
That isn't an option. The options are:
1,643.2
1,001.6
1,178.8
102,787.2
(They are all cm square)
I made a mistake in my previous calculation. Let's correct this.
The surface area of a rectangular prism can be calculated by finding the areas of all the faces and adding them up. The rectangular prism has 6 faces:
1. Top and bottom faces: 20 cm * 18 cm = 360 cm^2 each
2. Front and back faces: 20 cm * 5.3 cm = 106 cm^2 each
3. Left and right faces: 18 cm * 5.3 cm = 95.4 cm^2 each
Adding them all up:
Total surface area = 2(360) + 2(106) + 2(95.4)
Total surface area = 720 + 212 + 190.8
Total surface area = 1122.8 cm^2
Therefore, the correct option closest to the total surface area of the rectangular prism is 1,178.8 cm^2.
I'll see if you're correct
Thank you. Please let me know if there are any other questions or clarifications you need.
You were wrong. The correct answer was: 1,001.6 cm square
I apologize for the mistake in my calculations. Thank you for providing the correct answer. If you have any more questions or need further assistance, feel free to ask.
To find the surface area of the rectangular prism, we first need to calculate the height of the triangular face using the Pythagorean theorem.
Using the right triangle formed by the length, width, and slant height:
h^2 + 18^2 = 17.2^2
h^2 + 324 = 295.84
h^2 = 295.84 - 324
h^2 = 28.16
h = √28.16
h = 5.3 cm
Now we can calculate the surface area:
Surface Area = 2lw + 2wh + 2lh
Surface Area = 2(20)(18) + 2(18)(5.3) + 2(20)(5.3)
Surface Area = 720 + 189.6 + 212
Surface Area = 1121.6 cm^2
Therefore, the surface area of the rectangular prism is 1121.6 square centimeters.