# Surface Area of Cuboid (Definition, Formula & Examples)

The surface area of a 3D shape (solid object) is a measure of the total area that the surface of the object occupies. A cuboid is a 3D solid shape with six rectangular faces. The total surface area of a cuboid can be calculated if we calculate the area of the two bases and the area of the four lateral (side) faces. The change in any of the dimensions of cuboid changes the value of the surface area of a cuboid.

Let’s learn how to find the surface area of cuboid and its uses.

## What is the Surface Area of Cuboid?

The surface area of a cuboid is the sum of the area of the bases($2$ bases) and the area of lateral faces($4$ lateral faces) of the cuboid. Since the faces of the cuboid are made up of $6$ rectangles therefore the total surface area of the cuboid will be numerically equal to the sum of the areas of these six rectangles.

The surface area of a cuboid is measured as the “number of square units” ($cm^{2}$, $m^{2}$, $in^{2}$, $ft^{2}$, etc.). There are two types of surface areas

• Lateral Surface Area of cuboid
• Total Surface Area of cuboid

### Total Surface Area of Cuboid

The total surface area of cuboid or TSA Of Cuboid refers to the total area covered by all the faces of a cube. There are six rectangular faces in a cuboid, so to calculate TSA, we find the sum of the areas of these $6$ faces.

If the length, width(breadth), and height of a cuboid are $l$, $w$, and $h$ respectively, then the areas of the $6$ faces are

• Left face: $w \times h = wh$
• Right face: $w \times h = wh$
• Front face: $l \times h = lh$
• Back face: $l \times h = lh$
• Top face: $l \times w = lw$
• Bottom face: $l \times w = lw$

Total Surface Area (TSA) = (Area of left face) +  (Area of right face) +  (Area of front face) +  (Area of back face) + (Area of top face) + (Area of bottom face) = $wh + wh + lh + lh + lw + lw = 2wh + 2lh + 2lw = 2\left(lw + wh + hl \right)$.