Question

Please help
Find the surface area (show work)

Answer 1

The surface area of a shape is the total area of all the shapes that form the faces of a figure; it is the amount of area in total needed to form a three-dimensional shape (creating the faces).

Let’s first identify what shapes we have on the surface of the prism.

We have three pairs congruent rectangles. Congruent means exactly the same in every measurement, so the rectangles parallel from each other are congruent. Now, we know we are dealing with rectangles.

Recall the area of a rectangle formula:

A=L•W

So, using the definition of surface area and our observations of pairs of congruent rectangles, we can form the following formula to calculate surface area:

SA=2(L•W)+2(b•h)+2(L•h)

Now, let’s plug in the values into the formula:

SA=2(6•4)+2(6•5)+2(4•5)

Now, let’s simply using PEMDAS:

- Simplify parentheses first:

SA=2(24)+2(30)+2(20)

- Multiply all terms:

SA=48+60+40

- Add the terms:

SA=148

Therefore, the answer is:

The surface area is 148cm²

Answer 2

148 cm²

Explanation:

You want the surface area of a cuboid with edge lengths 4 cm, 5 cm, and 6 cm.

Area

The formula is shown in your problem statement.

It can be made easier to compute using a little rearranging:

SA = 2LW +2LH +2WH

SA = 2(LW +LH +WH)

SA = 2(LW +H(L +W))

The choice of dimensions for L, W, and H doesn't matter.

SA = 2(4·6 +5(4+6)) = 2(24 +5(10)) = 2(74) = 148 . . . . cm²

The surface area is 148 cm².