Question

A rectangular prism is cut along a diagonal on each face to create two triangular prisms. The distance between AA​ and BB​ is 55​ inches.

Answer 1

The surface area of the rectangular prism is 94 in² and the surface area of the two triangular prisms is 142 in².

What is of total surface area of the rectangular prism?

The total surface area of the rectangular prism is the space occupied by each of the face of it. It is the sum of area of all the faces of the prism.

Total surface area of the rectangular prism is calculated with the following formula.

$A=2(lb+bh+lh)$

Here, (b) is the breath of the base (l) is the length and (h) is the height of the rectangular prism.

A rectangular prism is cut along a diagonal on each face to create two triangular prisms. The distance between A​ and B​ is 5​ inches.

The length, width, and height of the prism is 5in, 3 in and 4 in long. Put these value in the above formula as,

$A=2(5\times3+3\times4+5\times4)\\A=2(15+12+20)\\A=2(47)\\A=94\rm\; in^2$

The formula for surface area of one triangle prism is,

$A_t=(a+b+c)l+bh$

Here, (a,b,c) are the sides of a triangle. The sides of the triangular face are 3 in, 4in and 5 in long. Thus, the surface area of it is,

$A_t=(4+3 +5)5+3\times4\\A_t=(12)5+12\\A_t=72\rm\;in^2$

For the two triangular prism,

$A_t=2\times72\\A_t=142\rm\; in^2$

Hence, the surface area of the rectangular prism is 94 in² and the surface area of the two triangular prisms is 142 in².

Learn more about the total surface area of a rectangular prism here;

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