Question

HELP ME PLEASE I BEG YOU!!

Answer 1

Surface area of the box is 304 square inches

Explanation:

Two different methods:

Method 1: Sum of the parts

Method 2: General formula for the Surface Area of a box

Method 1: Sum of the parts

For a box, there are 6 sides, all of which are rectangles:

• the front and back
• the left and right sides
• the top and bottom

Each of the above pairs has the same area.

The general formula for the area of a rectangle is
`A_(rectangle)=length*width`

As we look at different rectangles, the length of one rectangle may be considered the "width" of another rectangle, and that's okay as we calculate things separately. (We'll examine how to calculate everything at once in Method 2).

The area for the front/back side is 8in * 10in = 80 in^2

`A_(front)=A_(back)=80~in^2`

The area for the left/right side is 4in * 8in = 32 in^2

`A_(left)=A_(right)=32~in^2`

The area for the top/bottom side is 4in * 10in = 40 in^2

`A_(top)=A_(bottom)=40~in^2`

So, the total surface area is

`A_(Surface~Area) = A_(front) + A_(back) + A_(left) + A_(right) + A_(top) + A_(bottom)`

`A_(Surface~Area) = (80in^2) + (80in^2) + (32in^2) + (32in^2) + (40in^2) + (40in^2)`

`A_(Surface~Area) = 304~in^2`

Method 2: General formula for the Surface Area of a box

There is a formula for the surface area of a box:
`A_(Surface~Area~of~a~box) = 2(length*width + width*height + height*length)`

This formula calculates the area of one of each of the matching sides from the side pairs discussed in Method 1, adds those areas together (giving 3 of the sides), and doubles the result (bringing in the area for the matching missing 3 sides).

For clarity, let's decide that the "10 in" is the width, the "8 in" is the height, and the left over "4 in" is the length.

`A_(Surface~Area~of~the~box) = 2((4in)(10in) + (10in)(8in) + (8in)(4in))`

`A_(Surface~Area~of~the~box) = 2(40in^2 + 80in^2 + 32in^2)`

`A_(Surface~Area~of~the~box) = 2(152in^2)`

`A_(Surface~Area~of~the~box) = 304in^2`