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It is given that the length, breadth and height of the cuboid is $15{\text{ feet,12 feet}}$ and $9{\text{ feet}}$ and we have to find the total surface area of the cuboid. That is,

Length$\left( l \right) = 15{\text{ feet}}$

Breadth$\left( b \right) = 12{\text{ feet}}$

Height$\left( h \right) = 10{\text{ feet}}$

The total surface area of the cuboid is the sum of all the faces of the cuboid and we know that there are 6 faces in the cuboid.

Area of front and back face $\left( {{A_1}} \right) = \left( {{\text{Area of ABCD}}} \right) + \left( {{\text{Area of EFGH}}} \right)$

Area of front and back face $\left( {{A_1}} \right) = 2\left( {l \times h} \right)$

Substitute the values:

Area of front and back face $\left( {{A_1}} \right) = 2\left( {15 \times 10} \right) = 300$ square feet

Area of the upper and lower face $\left( {{A_2}} \right) = \left( {{\text{Area of ABFE}}} \right) + \left( {{\text{Area DCGH}}} \right)$

Area of the upper and lower face $\left( {{A_2}} \right) = 2\left( {l \times b} \right)$

Substitute the values:

Area of upper and lower face $\left( {{A_2}} \right) = 2\left( {15 \times 12} \right) = 360$square feet

Area of left and right face$\left( {{A_3}} \right) = \left( {{\text{Area of AEHD}}} \right) + \left( {{\text{Area of BCGF}}} \right)$

Area of left and right face $\left( {{A_3}} \right) = 2\left( {h \times b} \right)$

Substitute the values:

Area of left and right face$\left( {{A_3}} \right) = 2\left( {10 \times 12} \right) = 240$ square feet

So, the total surface area of the cuboid is given as:

The total surface area of a cuboid$ = {A_1} + {A_2} + {A_3}$

Put the values:

The total surface area of a cuboid$ = 300 + 360 + 240$

The total surface area of cuboid $ = 900$ square feet

Therefore, the total surface area of the cuboid is $900$ square feet.

$A = 2({\text{length}} \times {\text{breadth + breadth}} \times {\text{height + height}} \times {\text{length}})$

Substitute the values of length, breadth, and height of the cuboid into the formula:

$A = 2(15 \times 12 + 12 \times 10 + 10 \times 15)$

$A = 2\left( {180 + 120 + 150} \right)$

$A = 2\left( {450} \right)$

$A = 900$ Square feet

So, the total surface area of the cuboid is 900 square feet.