How to Calculate the Perimeter of a Trapezium Step by Step
Have you ever seen a trapezium shape in your daily life?
Is it Trapezium?
Can you mention a few examples of trapezium or trapezoid? Have a look at your surroundings and decide on the shape of a trapezium. Would you be able to find out any? A little bit confused between trapezium or trapezoid? No worries, you’ll learn the same here. Firstly, trapezium and trapezoid are the same in American and Canadian English, a trapezoid is a quadrilateral with at least one pair of parallel sides. A trapezoid is known as a trapezium in British and other forms of English.
Trapezium
A trapezium is a quadrilateral with one pair of parallel opposite sides, as defined by Euclidean geometry. Trapezium comes from the Greek word "trapeza," which means "table." So, the Trapezium is a four-sided shape with only two parallel sides.
Trapezium
A trapezium is a two-dimensional quadrilateral with a pair of parallel opposite sides (because of its four straight lines). The base and the non-parallel sides of the trapezium are referred to as the base and legs of the trapezium, respectively.
It has four sides and four corners and is a closed plane shape. The following is a diagram of a trapezium shape:
Trapezium WXYZ
In the above figure, XY and WZ are the bases while XW and YZ are the legs of the trapezium.
Properties of a Trapezium
Each quadrilateral has its unique set of characteristics that distinguish it from the other. These attributes provide extra information about a shape's geometrical construction. The following are the properties of trapezium:
It's a two-dimensional shape.
A trapezium's bases are parallel to one another.
A trapezium's diagonals are always intersected by each other.
The total of the adjacent internal angles is 180°.
In a trapezium, the sum of all internal angles is always 360°.
Trapezium Formula
Consider a trapezium with the lengths of parallel sides a and b units and the altitude "h."
Trapezium with the Lengths of Parallel Sides and the Altitude
Calculating the average of bases and multiplying the result by the altitude yields the trapezium area. As a result, trapezium area $= \left(\dfrac{AB + DC}{2}\right) AM = \left(\dfrac{a+b}{2}\right) h$, where AB, CD represent the bases and AM represents the altitude.
The perimeter of a trapezium is calculated by adding all of its sides together (because the perimeter is the sum of boundaries). As a result, the perimeter of a trapezium ABCD = AB + BC + CD + AD.
Solved Examples
1. If a trapezium is given with its three sides whose measures are 10cm, 12cm, and 7cm. Find the length of the fourth side of the trapezium if the perimeter is 40 cm.
Ans: Perimeter of trapezium = Sum of all its sides (all four sides) = 40 cm
Let the fourth side be ‘a’ cm.
Thus, applying the formula:
Perimeter is 40 = 10 + 12 + 7 + a
a = 40 – (10 + 12 + 7)
a = 40 – 29
a = 11 cm
Therefore, the length of the fourth side is 11 cm.
2. Seeta bought a trapezium-shaped table whose bases and legs are 25 cm,20 cm, 10 cm, and 12 cm respectively. She wants to know the perimeter of the table. Can you help her to find it?
Ans: Perimeter of trapezium = Sum of all its sides
So, applying the formula:
Perimeter of trapezium = 25 + 20 + 10 + 12
Perimeter of trapezium = 67 cm
Hence, the perimeter of the table is 67 cm.
Practice on your own:
Q1. The parallel sides of a trapezium are 25 cm and 11 cm, while its nonparallel sides are 15 cm and 13 cm. Find the perimeter of the trapezium.
Ans: 64 cm
Q2. What is the perimeter of the trapezoid in which the sum of lengths of non-parallel sides is 12 units, and the sum of the parallel sides is 8 units?
Ans: 20 units
Conclusion
Trapezium comes from the Greek word "trapeze," which means "table." So, the Trapezium is a four-sided shape with only two parallel sides. The perimeter of a trapezium is calculated by adding all of its sides together (because the perimeter is the sum of boundaries). As a result, the perimeter of a trapezium ABCD = AB + BC + CD + AD.
FAQs on Perimeter of a Trapezium: Definition, Formula & Examples
1. What is the basic formula to calculate the perimeter of a trapezium?
The formula for the perimeter of a trapezium is the sum of the lengths of all its four sides. If the sides of a trapezium are labelled as a, b, c, and d, the perimeter (P) is calculated as: P = a + b + c + d. Unlike the area formula, you do not need to distinguish between parallel and non-parallel sides to find the perimeter.
2. Can you provide a simple example of calculating the perimeter of a trapezium?
Certainly. Imagine a trapezium with side lengths of 5 cm, 7 cm, 8 cm, and 10 cm. To find its perimeter, you simply add these lengths together.
Perimeter = 5 cm + 7 cm + 8 cm + 10 cm = 30 cm.
So, the total length of the boundary of this trapezium is 30 cm.
3. What defines a shape as a trapezium in geometry?
A trapezium (also known as a trapezoid in American English) is a quadrilateral, which is a four-sided polygon, defined by one key property: it must have at least one pair of opposite sides that are parallel to each other. These parallel sides are called the bases of the trapezium, while the other two non-parallel sides are called the legs.
4. What are the key properties of a trapezium?
A trapezium has several distinct properties that are consistent with the CBSE curriculum for classes 7-9. These include:
- It is a two-dimensional closed figure with four sides.
- It has exactly one pair of parallel sides, known as the bases.
- The non-parallel sides (legs) can be of different lengths.
- The sum of all four interior angles is always 360 degrees.
- The sum of the adjacent angles between one parallel side and a leg is 180 degrees.
- The diagonals of a trapezium intersect each other.
5. How does finding the perimeter of a trapezium differ from finding the perimeter of a parallelogram?
Fundamentally, the method is the same: you sum the lengths of all four sides for both shapes. However, the properties of a parallelogram simplify the calculation. A parallelogram has two pairs of equal-length opposite sides. So, if its adjacent sides are 'a' and 'b', its perimeter is 2(a + b). A general trapezium may have four sides of different lengths, so you must know all four individual lengths to sum them up as a + b + c + d.
6. How can you find the length of a missing side of a trapezium if the perimeter and the other three sides are known?
You can find the missing side using a simple algebraic subtraction. Since the perimeter is the total sum of all sides, subtract the sum of the three known sides from the total perimeter. For instance, if the perimeter is 50 cm and the known sides are 10 cm, 12 cm, and 15 cm, the calculation would be:
Missing Side = 50 cm - (10 cm + 12 cm + 15 cm) = 50 cm - 37 cm = 13 cm.
7. What is an isosceles trapezium and does it have a special perimeter formula?
An isosceles trapezium is a special type of trapezium where the two non-parallel sides (legs) are equal in length. While the general formula (sum of all sides) still applies, this property simplifies the calculation if you know the lengths of the bases and one leg. If the parallel bases are 'a' and 'b', and the length of one equal leg is 'c', the perimeter (P) can be calculated as: P = a + b + 2c.
8. In what real-world situations might you need to calculate the perimeter of a trapezium?
Calculating the perimeter of a trapezium is useful in various practical scenarios. For example, you might need it for:
- Fencing a garden or a plot of land that has a trapezoidal shape.
- Putting a decorative border around a tabletop or a mirror with a trapezoid design.
- Calculating the amount of material needed for the frame of a window or a piece of art that is shaped like a trapezium.
- Determining the length of track required for the boundary of a trapezoidal park or play area.
