Question

A triangular prism has bases that are equilateral triangles. Which statements are true about the surface area of the triangular prism? Choose all that apply. A all three rectangular faces have the same surface area

B the surface area of each rectangular face is 66cm2
C the combined surface area of both bases is greater than the surface area of one rectangular face
D the surface area of one base is 15.6cm2

Answer 1

C.

D.

B.

C.

A.

D.

C.

C.

B.

A. B. and D.

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Answer 2

A. all three rectangular faces have the same surface area

B. the surface area of each rectangular face is
`66\ cm^(2)`

D. the surface area of one base is
`15.6\ cm^(2)`

Explanation:

Verify each statement

case A) all three rectangular faces have the same surface area

The statement is true

Because, the equilateral triangle has the three equal sides and the three equal internal angles.

case B) the surface area of each rectangular face is
`66\ cm^(2)`

The statement is true

Because, the area of each rectangular face is equal to

`6(11)=66\ cm^(2)`

case C) the combined surface area of both bases is greater than the surface area of one rectangular face

The statement is False

Because

The combined surface area of both bases is
`2[(1)/(2)(6)(5.2)]=31.2\ cm^(2)`

The surface area of one rectangular face is
`66\ cm^(2)`

therefore

`31.2\ cm^(2)< 66\ cm^(2)`

case D) the surface area of one base is
`15.6\ cm^(2)`

The statement is True

Because

The surface area of one base is
`(1)/(2)(6)(5.2)=15.6\ cm^(2)`