Question

What is the total surface area of the figure shown?

Answer 1

3(20×9)+3((24-9)×8)+(10×8)+(9×10)+((20-8)×10)+((24-9)×10)

=3(180)+3(15×8)+80+90+(12×10)+(15×10)

=540+3(120)+170+120+150

=920+360

=1280

Answers

`{1280cm}^(2)`

Answer 2

`S=1964 in^(2)`

Explanation:

The surface of a rectangular prims is defined as

`S=2lw+2wh+2lh`

Where
`l` is length,
`w` is width and
`h` is height.

In this case, we have a figure formed by two rectangular prism. We are gonna call Surface 1 to the bottoming prism.

Its diemensions are:

`l=24in\\w=10in\\h=8in`

So, the Surface 1 is

`S_(1)=2(24)(10)+2(10)(8)+2(24)(8)= 480+160+384=1024in^(2)`

Now, the dimensions of Surface 2 are

`l=9in\\w=10in\\h=20in`

Replacing all values, its surface is

`S_(2)= 2(9)(10)+2(10)(20)+2(9)(20)=180+400+360=940in^(2)`

Therefore, the total surface of the whole figure is

`S=1024+940=1964 in^(2)`