Question

What is the total surface area of the figure shown

Answer 1

I think the answer is 3912.

Answer 2

Answer: The total surface area is 2784 sq. inches.

Step-by-step explanation: We are given to find the total surface area of the given figure.

Let us divide the figure into two two cuboids 1 and 2 as shown in the attached figure.

We know that the surface area of a cuboid with length 'l', breadth 'b' and height 'h' is given by

`S.A.=2(l_1b_1+l_1h_1+h_1b_1).`

The dimensions of the cuboid 1 are

`length,~l_1=14~\textup{inches},\\\\breadth,~b_1=12~\textup{inches},\\\\height,~h_1=24-10=14~\textup{inches}.`

The dimensions of the cuboid 2 are

`length,~l_2=30~\textup{inches},\\\\breadth,~b_1=14~\textup{inches},\\\\height,~h_1=10~\textup{inches}.`

Therefore, surface area of cuboid 1 is given by

`S.A_1\\\\=2(l_1b_1+l_1h_1+h_1b_1)\\\\=2(14* 12+14* 14+14* 12)\\\\=2(532)\\\\=1064~\textup{sq. inches.}`

And surface area of cuboid 2 is given by

`S.A_2\\\\=2(l_2b_2+l_2h_2+h_2b_2)\\\\=2(30* 14+30* 10+14* 10)\\\\=2(420+300+140)\\\\=2(860)\\\\=1720~\textup{sq. inches}.`

Thus, the total surface area of the figure is

`S.A.=S.A_1+S.A_2=1064+1720=2784~\textup{sq. inches}.`