Find the surface area of the composite solid.

Option B is correct.

Step-by-step explanation:

Given:

A Solid Figure made up pf cuboid and a triangular based prism.

To find: Total Surface area of the figure.

Total Surface Area = Area of front + Area of top + Area of Back + 2 × Area of side + Area of bottom

Area of Front = Area of Square + Area of rectangle

                      = 10 × 10

                      = 100 in.²

Area of top = Area of Rectangle

                   = 13 × 10

                   = 130 in.²

Area of back =  Area of square in down + Area of rectangle in up

                      = 10 × 10 + 5 × 10

                      = 100 + 50

                      = 150 in.²

Area of the bottom = Area of the rectangle

                                = 12 × 10

                                = 120 in.²

Area of the side = Area of rectangle + Area of the triangle

                           = 12 × 10 + 1/2 × 5 × 12

                           = 120 + 5 × 6

                           = 120 + 30

                           = 150 in.²

Total Surface Area = 100 + 130 +150 + 120 + 2 × 150

                               = 500 + 300

                               = 800 in.²

Therefore, Option B is correct.