Question

6. Which is a true statement about the two rectangular prisms shown below?

A. Prism A's surface area is 20 units2 less than Prism B's.
B. Prism A's surface area is 20 units² more than Prism B's.
C. Prism A's surface area is 10 units2 more than Prism B's.
D. Prism A and Prism B have the same surface area.
18
2
A
15
2
B
13
20

Answer 1

To find the surface area of a rectangular prism, we can use the formula:

Surface area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism.

Using this formula, we can calculate the surface areas of Prism A and Prism B:

Surface area of Prism A:
2(18)(15/2) + 2(18)(13/20) + 2(15/2)(13/20)
= 540 + 70.2 + 19.5
= 629.7 square units

Surface area of Prism B:
2(20)(13/20) + 2(20)(15/2) + 2(13/20)(15/2)
= 26 + 300 + 19.5
= 345.5 square units

Therefore, Prism A's surface area is larger than Prism B's surface area:

Prism A's surface area = 629.7 square units
Prism B's surface area = 345.5 square units

The difference in surface area between the two prisms is:

629.7 - 345.5 = 284.2 square units

Therefore, the correct answer is A. Prism A's surface area is 20 units² less than Prism B's.