Surface area of rectangular prism answer key

To see what is the surface area of a rectangular prism, we need to know all three of its sides. Let's start with the notation we use for them and for the other values in our surface area of a rectangular prism calculator:

Table of Contents Show

What is the surface area of the rectangular prism?
What is the formula for surface area of a rectangle?
How do you find the surface area of a rectangular prism worksheet?

l – the first base edge length;
w – the second base edge length;
h – the lateral edge length (also called the height of the prism);
A_b – the base area of the prism;
A_l – the lateral area of the prism;
A – the surface area of the prism; and
V – the volume of the prism.

Note that A_b denotes the surface area of a single base of our prism. On the other hand, A_l denotes the lateral area, meaning the total area of the four lateral faces. Therefore, since the solid has two bases (the bottom one and the top one), the surface area of a rectangular prism formula is as follows:

surface_area = 2 × base_area + lateral_area,

which, in our notation, translates to

A = 2 × A_b + A_l.

Recall that all the faces in our calculator are rectangles, and, as mentioned in the rectangle area calculator, they are calculated by multiplying the side lengths. Now, let's use that information to study the base of our prism. With our notation, it is a rectangle with sides l and w, so its area is l × w. And that is precisely the formula for the base area:

A_b = l × w.

Piece of cake, wasn't it? Well, let's now try to do something a little bit more complicated and move on to the lateral area. We have four faces contributing to that number, and all of them are rectangles. What is more, among the four, there are two pairs of identical ones (the front and back wall and the left and right wall). All of those have one side equal to h, the lateral edge (or the height) of the prism. Also, the other side of one of the pairs is equal to the first base edge, say l, and the other is equal to the length of the second one, which is w. All in all, we obtain that the lateral area, or A_l as we call it, is

A_l = l × h + l × h + w × h + w × h,

or simply

A_l = 2 × l × h + 2 × w × h.

Observe that, together with the base area, this allows us to translate the surface area of a rectangular prism formula into

A = 2 × A_b + A_l = 2 × l × w + 2 × l × h + 2 × w × h.

What is the surface area of the rectangular prism?

Therefore, the lateral surface area (LSA) of a rectangular prism = 2 ( l + w ) h square units. Therefore, the surface area of a rectangular prism formula is given as, Surface Area of a rectangular prism = 2 (lh +wh + lw ) Square units.

What is the formula for surface area of a rectangle?

The rectangle below has a length of 4 inches and a width of 3 inches. Calculate the surface area using the area formula. Answer: The area can be calculated using the formula A=l×w, where A represents area, l represents length, and w represents width.

How do you find the surface area of a rectangular prism worksheet?

It is a solid shape with 6 rectangular faces. The length l, width w, and height h are expressed in whole numbers. Apply the formula SA = 2(lw + lh+ wh), find the surface area, and represent the answer in square units.