The surface area of a cuboid is the total space occupied by all its surfaces/sides. In geometry, a three-dimensional shape having six rectangular faces is called a cuboid. A cuboid is also known as a regular hexahedron and has six rectangular faces, eight vertices, and twelve edges with congruent, opposite faces. It is a three-dimensional form of a rectangle with four lateral faces and two faces at the top and bottom. Some examples of cuboids that we regularly see are bricks, geometric boxes, shoe boxes, packaging boxes, etc. Let’s learn in detail about the surface area of a cuboid, along with examples. Show What is the Surface Area of a Cuboid?The surface area of a cuboid is the total area covered by all of its surfaces, and since the cuboid is the 3-D form of a rectangle, therefore, along with length and breadth, the height of the cuboid is also involved in finding the surface area. Surface area and volume are calculated in 3-D figures. The surface area of a cuboid is measured in square units (For example, cm2, m2, etc). A cuboid has 2 kinds of surface area. The surface area of a cuboid is calculated based on what type of surface area is required. The formulas for both types of surface areas are different. They are:
The total surface area of a cuboid is the area of all 6 sides of the cuboid. However, the lateral surface area of a cuboid is the area of only 4 sides (base and top excluded). Imagine there is a room in the shape of a cuboid; if only the walls of the room (excluding the ceiling) require painting, then the lateral surface area of the room will be taken into account for the paint used, and the total surface area of the room is the sum of the 4 walls + ceiling + floor. Both the total surface area and lateral surface area of a cuboid are calculated in terms of length (l), breadth(b), and height(h). The formulas are:
The lateral and total surface areas of a cuboid are the two types of surface areas of a cuboid. The lateral surface area of a cuboid is the area occupied by its lateral faces, whereas the total surface area of a cuboid is the area occupied by all its six rectangular faces. Total Surface Area of CuboidThe total surface area of a cuboid can be calculated by first calculating the area of all the sides and then adding all six sides. Let us consider that “l” is the length of the cuboid, “b” is the breadth of the cuboid, and “h” is the height of the cuboid. We know that in a cuboid, opposite faces are equal, i.e., ABCD = PQRS, APSD = BQRC, and ABQP = DCRS. Now, the total surface area of the cuboid is equal to the sum of the areas of its six rectangular faces. The total surface area of the cuboid = Area of [ABCD + APSD + ABQP + PQRS + BQRS + DCRS]. Area of [ABCD +APSD + ABQP + ABCD +APSD + ABQP] = 2 Area of [ABCD +APSD + ABQP]
Therefore,
Lateral Surface Area of a CuboidThe lateral surface area of a cuboid is the area occupied by its lateral faces. Hence, the lateral surface area of the cuboid = The total surface area of the cuboid – The area of the top and bottom faces of the cuboid = 2 (lb + bh + lh) – Area of [ABPQ + CDRS} = 2 (lb + bh + lh) – 2 Area of (ABPQ) = 2 (lb + bh + lh) – 2lb = 2 (bh + lh) = 2h(l + b) Hence,
How to Find the Surface Area of Cuboid?The surface area of a cuboid is the total area of all the sides/surfaces of the cuboid. In order to understand how to find the surface area of a cuboid, let’s take a look at the given steps: Step 1: Observe and note down the dimensions of each size. In case the dimensions have different units, convert them into one unit. Step 2: Use the formula for the total surface area of the cuboid: that is, TSA = 2 (lb + bh + lh) square units Step 3: Note down the area contained in proper units. Let’s consider an example to determine the surface area of the cuboid using its formula. Example: Calculate the total surface area of a cuboid if its length, breadth, and height are 8 cm, 3 cm, and 5 cm, respectively. Solution:
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Solved Examples on Surface Area of a CuboidExample 1: Determine the lateral surface area of a cuboid if its length, breadth, and height are 15 in, 8 in, and 12 in, respectively. Solution:
Example 2: What is the total surface area of a cuboid shown in the figure below: Solution:
Example 3: Calculate the height of the cuboid whose lateral surface area is 360 square units and whose length and breadth are 12 units and 8 units, respectively. Solution:
Example 4: Determine the length and the total surface area of a cuboid whose lateral surface area is 960 sq. in and whose breadth and height are 12 in and 16 in, respectively. Solution:
Example 5: Calculate the total surface area of a cuboid if its length, breadth, and height are 10 in, 5 in, and 8 in, respectively. Solution:
Example 6: Determine the lateral and total surface areas of a cuboid whose length, breadth, and height are 21 cm, 16 cm, and 18 cm, respectively. Solution:
FAQs on Surface Area of a CuboidQuestion 1: What is the difference between the total surface area of a cuboid and the lateral surface area of a cuboid? Answer:
Question 2: What do you mean by TSA and LSA of a cuboid? Answer:
Question 3: What is the unit used for the surface area of a cuboid? Answer:
Question 4: What is the total surface area of a cuboid? Answer:
Question 5: How to find the lateral surface area of a cuboid? Answer:
Question 6: Find the volume and surface area of a cuboid. Answer:
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