Area of Trapezium, Know its Formula

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Discover the Area of Trapezium and know the formula, properties, and practical applications of a trapezium. Uncover the secrets behind calculating the area of this unique quadrilateral shape and gain insights into its significance in various fields.

Area of Trapezium

To find the area of a trapezium, you need to know the lengths of the parallel sides and the height of the trapezium. Let’s assume the lengths of the parallel sides are “a” and “b,” and the height is “h.”

The formula to calculate the area of a trapezium is:

Simply substitute the values of “a,” “b,” and “h” into the formula, and perform the calculation to find the area of the trapezium.

Area of Trapezium Formula without Height

The formula for calculating the area of a trapezium (also known as a trapezoid) without the height is not possible because the height is an essential parameter required to calculate the area of a trapezium.

The general formula for calculating the area of a trapezium is:

• Area = (1/2) × (a + b) × h

where:

a and b are the lengths of the parallel sides of the trapezium

h is the height (the perpendicular distance between the parallel sides)

Without the height, it is not possible to determine the area of a trapezium. The height is necessary because it represents the extent of the trapezium perpendicular to the parallel sides and determines the area enclosed within the shape.

What is the Area of a Trapezium Formula with Examples?

The formula to calculate the area of a trapezium (also known as a trapezoid) is:

• Area = (1/2) × (a + b) × h

Where:

• “a” and “b” are the lengths of the parallel sides (also known as the bases) of the trapezium.
• “h” is the perpendicular distance between the parallel sides.
• To find the area, you add the lengths of the parallel sides, divide by 2, and then multiply by the height.

Let’s consider a few examples:

Example 1:

Given a trapezium with base lengths of 4 cm and 8 cm, and a height of 6 cm, the area can be calculated as follows:

Area = (1/2) × (4 cm + 8 cm) × 6 cm

= (1/2) × 12 cm × 6 cm

= 6 cm × 6 cm

= 36 cm²

Therefore, the area of the trapezium is 36 square centimeters.

Example 2:

Suppose you have a trapezium with base lengths of 12 meters and 18 meters, and a height of 5 meters. To calculate the area, you can use the formula:

Area = (1/2) × (12 m + 18 m) × 5 m

= (1/2) × 30 m × 5 m

= 15 m × 5 m

= 75 m²

The area of this trapezium is 75 square meters.

Remember to use consistent units for all the measurements to obtain accurate results.

What are the Properties of Trapezium?

A trapezium, also known as a trapezoid in some countries, is a quadrilateral with at least one pair of parallel sides. Here are some of the properties of a trapezium:

• Parallel sides: A trapezium has two opposite sides that are parallel to each other.
• Non-parallel sides: The other two sides of a trapezium are not parallel to each other.
• Base: The parallel sides of a trapezium are called the bases. The longer base is typically referred to as the “bottom base,” and the shorter base is called the “top base.”
• Legs: The non-parallel sides of a trapezium are called the legs or the lateral sides.
• Angles: A trapezium has four angles. The angles on the same side of the trapezium and adjacent to its parallel sides are called consecutive angles. The angles on the opposite sides of the trapezium are called opposite angles.
• Adjacent angles: The consecutive angles of a trapezium are supplementary, which means their measures add up to 180 degrees.
• Median: The median of a trapezium is the line segment connecting the midpoints of the legs. It is parallel to the bases and its length is the average of the lengths of the bases.
• Height: The height (or altitude) of a trapezium is the perpendicular distance between the bases. It is a straight line segment that extends from one base to the other.
• Area: The area of a trapezium can be calculated using the formula: Area = (1/2) × (sum of bases) × height.
• Diagonals: A trapezium has two diagonals that connect the non-adjacent vertices. Unlike a parallelogram, the diagonals of a trapezium do not bisect each other.

These are some of the key properties of a trapezium. Remember that terminology and specific definitions may vary in different regions.

What are the Two Bases of a Trapezium?

In a trapezium (also known as a trapezoid in some countries), the bases are the two parallel sides of the shape. Let’s denote the bases as “base 1” and “base 2”. Base 1 is typically the longer side, while base 2 is the shorter side. The non-parallel sides of a trapezium are called the legs or the lateral sides.

Example of a Real-life Situation where the Area of a Trapezium is Relevant

One real-life situation where the area of a trapezium is relevant is in the construction industry, particularly when calculating the amount of material needed for a sloping roof or a land leveling project.

Let’s say a construction company is tasked with building a roof for a house. The roof has a trapezoidal shape, where the two parallel sides represent the lengths of the roof, and the non-parallel sides represent the widths. To determine the area of the roof, the construction company would use the formula for the area of a trapezium:

where ‘a’ and ‘b’ are the lengths of the parallel sides (bases) of the trapezium, and ‘h’ is the vertical height between the bases.

By calculating the area of the trapezoidal roof, the construction company can estimate the amount of roofing material required, such as shingles or metal sheets, to cover the entire surface. This information helps them accurately budget for the materials needed and provide cost estimates to the client.

Similarly, in land leveling projects, where irregularly shaped pieces of land need to be flattened or prepared for construction, the area of trapeziums can be used to calculate the amount of earthwork required. By determining the area of individual trapezoidal sections within the land plot, the construction team can estimate the volume of soil that needs to be removed or added to achieve the desired surface level.

In both cases, understanding the concept of trapeziums and their areas is crucial for accurate calculations in the construction industry, helping to streamline project planning and ensure the appropriate allocation of resources.

How does the Area of a Trapezium Compare to the Area of a Rectangle with the Same Bases and Height?

The area of a trapezium and a rectangle with the same bases and height are not the same.

A trapezium is a quadrilateral with one pair of parallel sides, called the bases. The height of the trapezium is the perpendicular distance between the bases. The formula to calculate the area of a trapezium is given by:

• Area = (1/2) × (sum of bases) × height

On the other hand, a rectangle is a quadrilateral with all four angles equal to 90 degrees. The formula to calculate the area of a rectangle is given by:

If we consider a trapezium with bases of length “a” and “b” and height “h,” and a rectangle with the same bases and height, the area of the trapezium would be smaller than the area of the rectangle, except in the special case where the trapezium is actually a rectangle (i.e., when the non-parallel sides are perpendicular to the bases). In all other cases, the trapezium will have a smaller area due to its slanted sides.

The area of a trapezium with the same bases and height as a rectangle will generally be smaller than the area of the rectangle, unless the trapezium is a rectangle itself.

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