Length, Width, and Height: Dimensions shape how we interact with the world. At their core are length, breadth, and height, simple yet fundamental measurements. Length captures the longest side, like the span of a table.
Breadth or width measures the distance across, perpendicular to length. Height gauges how tall something stands, reaching vertically. Together, they define the size, space, and structure of everything around us, from boxes to buildings. Understanding these three dimensions helps us visualize, design, and organize with precision.
What Are Length, Width, and Height?
Length, width, and height are dimensions for measuring an object's size. In two-dimensional (2D) shapes, we use length and breadth. In three-dimensional (3D) shapes, we incorporate height along with length and width.
Isosceles Triangle
Length
Length represents the longest horizontal measurement of an object. It tells us how long the object is from one end to the other. This dimension is used to determine the maximum extent of an object along a straight line. For example, in a rectangular table, the side that stretches the furthest is considered its length. Length is typically measured in units such as meters (m), centimeters (cm), millimeters (mm), inches (in), or feet (ft), depending on the context and scale of measurement. Length Examples
- Measuring Furniture: When buying a sofa, you might measure its length to ensure it fits against your wall. For instance, a sofa might be 2 meters long .
- Road Distances: The distance between two towns or cities is often described in kilometers. For example, "The length of the road from City A to City B is 150 km ."
- Personal Height Measurement: When measuring a person’s height, the measurement represents the length of their body from head to toe.
Width ( Breadth)
Width , also called breadth , is the shorter horizontal measurement of an object, running perpendicular to the length. It measures how wide or broad the object is from side to side.
Width complements the length and is used when describing objects that are not just long but also have a breadth to them. Width is measured using the same units as length, such as meters, centimeters, inches, or feet .
Breadth Examples
- Measuring a Table: If a table has a length of 2 meters and a width of 1 meter , the width tells us how broad the table is from side to side.
- Books and Notebooks: The width of a standard book might be 15 cm , while its length might be 25 cm .
- Smartphones: A phone with a width of 7 cm and a length of 15 cm indicates how broad the device is when held horizontally.
Height (Depth)
Height refers to the vertical measurement of an object, indicating how tall or deep it is. In some contexts, particularly when measuring downward, height is referred to as depth . Height is the dimension that runs perpendicular to both length and width. Common units for measuring height include meters (m), centimeters (cm), inches (in), and feet (ft).
Height Examples
- Buildings: The height of a skyscraper might be 300 meters , indicating how tall the structure is from the ground to the top.
- Swimming Pools: The depth of a swimming pool might be 2 meters , describing how deep the pool is from the surface of the water to the bottom.
- Children's Growth: A child’s height might be measured at 120 cm , representing their vertical growth.
Perimeter of a Triangle
Length, Width, and Height Key Differences
To better understand these dimensions, let’s summarize the differences between length, width, and height:
| Aspect |
Length |
Width (Breadth) |
Height (Depth) |
| Definition |
Longest horizontal dimension |
Shorter horizontal dimension |
Vertical dimension |
| Direction |
Horizontal, longest side |
Horizontal, shorter side |
Vertical (upward or downward) |
| Orientation |
Along the object's maximum extent |
Perpendicular to length |
Perpendicular to both length and width |
| Common Units |
m, cm, in, ft |
m, cm, in, ft |
m, cm, in, ft |
| Example Object |
Length of a table (e.g., 2 m) |
Width of a table (e.g., 1 m) |
Height of a table (e.g., 0.8 m) |
| Applications |
Measuring distance, furniture, roads |
Measuring screens, books, and doorways |
Measuring buildings, shelves, water depth |
How Do Length, Width, and Height Work Together?
Length, width, and height work together to define a three-dimensional object’s size, volume, and surface area . For example, a box with dimensions 30 cm × 20 cm × 15 cm is 30 cm long , 20 cm wide , and 15 cm high . These dimensions help calculate:
Volume: Volume tells us how much space the object occupies, expressed in cubic units like cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³).
The formula for the volume of a rectangular prism (cuboid) is: = Length × Width × Height
Surface Area: Surface area represents the total area required to cover the object's surfaces, expressed in square units like square meters (m²), square centimeters (cm²), or square inches (in²).
The formula for the surface area of a cuboid is = 2×(Length × Width + Length × Height + Width × Height)
Triangles
Example 1: Volume of a Rectangular Box
Imagine a rectangular box with the following dimensions:
- Length: 15 cm
- Width: 10 cm
- Height: 5 cm
These measurements provide a complete description of the box:
- The length (15 cm) tells us how long the box is.
- The width (10 cm) shows how wide it is.
- The height (5 cm) indicates how tall the box stands.
Together, these dimensions allow us to calculate the volume of the box using the formula:
Volume= Length × Width × Height
Substituting the values:
Volume = 15 cm × 10 cm × 5 cm = 750 cm 3
This means the box can hold 750 cubic centimeters of material.
Surface Area of a Rectangular Box
To calculate the surface area of the box, use the formula:
Surface Area = 2×(Length × Width + Length × Height + Width ×Height)
Substituting the values:
Surface Area=2×(15 cm ×10 cm +15 cm ×5 cm +10 cm ×5 cm)
Calculating each term:
15 ×10 = 150 cm 2 15 × 5 = 75 cm 2 10×5 = 50 cm 2
Adding them together:
150 + 75 + 50 = 275 cm 2 Now multiply by 2: 2 × 275 = 550 cm 2 The surface area of the rectangular box is 550 square centimeters. This represents the total area needed to cover all six faces of the box.
Example 2: Finding the Missing Dimension
The volume of a cuboid is 144 cubic cm. The length is 12 cm, and the width is 2 cm. Find the height.
Solution:
Using the volume formula: Length × Width × Height Substituting the values, we get: 144 = 12 ×2 × Height
Simplify:
144 = 24 × Height Height = 144/24
Answer: The height of the cuboid is 6 cm .
Practical Applications of Length, Width, and Height
Let’s explore the real-life applications of length, width, and height:
Architecture and Construction
In construction projects, accurate measurements of length, width, and height are essential. For example, when designing a building, architects specify:
- The length of walls and beams
- The width of rooms and corridors
- The height of ceilings and structures
These dimensions ensure that the structure is functional, safe, and aesthetically pleasing.
Packaging and Shipping
In logistics, understanding dimensions is critical for packaging and shipping. Companies measure the length, width, and height of boxes to:
- Calculate the volume for shipping costs
- Ensure products fit into packaging appropriately
- Optimize storage space in warehouses
Interior Design
When arranging furniture in a room, designers consider:
- The length of sofas, tables, and shelves
- The width of doorways and walkways
- The height of cabinets, curtains, and wall hangings
Length, width, and height are used to describe the size of 3D objects. Length is the longest horizontal side, width is the shorter horizontal side, and height is how tall the object is. Together, they help us understand the shape of an object, calculate how much space it takes up (volume), and complete tasks like designing spaces or packaging items. Join Online Classes for Kids now!!
