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Total area of the given prism is (104 + 16√13) Square inches.

Step-by-step explanation:

By the given diagram,

In the right triangular prism,

The sides of the base ( right triangle ) are 4 inches and 6 inches,

We have to finds : T.A. ( the total area of the prism )

Thus, the total base area of the prism = 2 ×  ( Area of triangle having base 4 inches and height 6 inches )

= 2× ( 1/2 × 4 × 6 )

= 4 × 6

= 24 square inches,

Let the hypotenuse of the triangles having sides 4 and 6 is x inches, ( shown in the diagram )

Thus, by the given diagram,

Now, the total lateral area of the prism,

= 8×2√13 + 8×4 + 8×6

= 16√13 + 32 + 48

= (16√13 + 80) square inches,

Since, the total area of the given prism (T.A.) = Total base area of the prism(B.A.) + Total lateral area ( L.A.)

= 24 + 16√13 + 80

= (104 + 16√13) Square inches.

d is the correct answer

step-by-step explanation:

x= 8 because 3x = 3 * 8, and 3*8 = 24

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