- 1-800-665-6601
- [email protected]

A rectangular prism consists of 2 rectangular bases and 4 rectangular sides. The bases are congruent and parallel to each other. Since every prism is a polyhedron (solid with flat faces), hence it does not consist of any curved sides. The same is applied to a rectangular prism and hence it is also a polyhedron with no curved sides. A rectangular prism has 8 vertices, 6 faces and 12 edges as shown in the figure below.

We can find plenty of examples of rectangular prisms in the world, including the very room we are sitting in. Some of the examples are skyscraper buildings, a room, a box etc.

Let the length be = l, width = w, and height = h.

Then the diagonal of a rectangular prism, d = √(l2 + w2 + h2).

Given that length l = 7m, width w = 4m and height, h = 3m.

Diagonal of a rectangular prism, d = √(l2 + w2 + h2).

Hence applying the above formula, we get: d = √(72 + 42 + 32).

This gives us d = √(49 + 16 + 9) = √74.

Now, √74 can be approximated to its decimal value as 8.6m.

Hence 8.6m is the diagonal length of the given rectangular prism!

We can find the lateral area of the rectangular prism using the formula as shown below:

Lateral Area of a Rectangular Prism = Perimeter of the Base * Height

L = P * h

Since we are finding lateral area of a rectangular prism, hence the perimeter of the base is nothing but the perimeter of the base rectangle. We know that the perimeter of a rectangle is the sum of all its sides. This gives us that the Perimeter of a rectangle, P = 2l + 2w (where l = length and w = width) of the rectangular prism.

Hence the Lateral Area of a Rectangular prism can now also be written as:

L = P * h

L = (2l + 2w) * h

Or L = 2lh + 2wh

(l = length, w = width, h = height)

Given that length l = 7m, width w = 4m and height, h = 3m.

Lateral area of the rectangular prism, L = Perimeter of the base * Height

L = 2lh + 2wh ==> L = (2* 7* 3) + (2* 4 * 3) ==> L = 42 + 24 = 66

Hence, the Lateral Area, L = 22m * 3m = 66m2 or 66 square meters.

In order to calculate the surface area of a rectangular prism, we use the formula as shown below:

S = L + (2 * B)

Since the Lateral area is 2lh + 2wh, we can plug-in its formula in the place of ‘L’. Now, the area of the base is nothing but the area of the base rectangle. Area of a rectangle = length * width. Therefore, the area of the base, B = l * w

Hence the Surface Area of a Rectangular prism can now also be written as:

S = L + (2 * B)

(Since L = 2lh + 2wh and B = l*w)

S = 2lh + 2wh + 2lw

(l = length, w = width, h = height)

Given that length l = 6m, width w = 3m and height, h = 5m.

Surface Area of the rectangular prism, S = 2lh + 2wh + 2lw

Hence, S = (2* 6* 5) + (2* 3* 5) + (2 * 6 * 3) ==> S = 60 + 30 + 36 = 126m2

In order to find the Volume of a rectangular prism, we can use the below formula:

Given the length = l, width = w and height = h

Volume of a rectangular prism, V = length * width * height

V = l * w * h

Given that length l = 6m, width w = 3m and height, h = 5m.

Volume of the rectangular prism, V = l * w * h

Hence, Volume, V = 6m * 3m * 5m = 90m2

A rectangular prism, also known as a cuboid is a prism consisting of rectangles as its surfaces. It is a 3-dimensional geometric shape just like any other prism, since it consists of length, width and height. A rectangular prism has its bases as rectangles and hence its name. The total surface area of a rectangular prism is the sum of the areas of all the surfaces and the volume of a rectangular prism is the measure of space contained inside the prism.

Given the length of the rectangular prim, l = 4m

Width of the rectangular prism, w = 1.5m

Height of the rectangular prism, h = 3m

Volume of a rectangular prism, V = (length) * (width) * (height)

Hence, volume of the rectangular prism, V = 4m * 1.5m * 3m = 18m3

Therefore, the volume of the given rectangular prism = 18m3

Given the length of the rectangular prim, l= 4m

Width of the rectangular prism, w= 1.5m

Height of the rectangular prism, h= 3m

Total Surface area of the rectangular prism, A = 2lw + 2lh + 2wh

Hence Area, A = (2* 4* 1.5) + (2* 4* 3) + (2* 1.5* 3)

Area, A= 12+ 24+ 9= 45

Hence, Surface area of the rectangular prism, A = 45m2