- Area = (1/2) x h x (a + b), where a and b are the two parallel sides and h is the perpendicular height
- An isosceles trapezium has equal non-parallel sides and equal base angles
- The sum of all interior angles in any trapezium is 360 degrees.
A trapezium (or trapezoid) is a quadrilateral consisting of one pair of parallel sides. It is a 2D shape with four sides. The area of any shape is defined as the region enclosed by its boundaries.
A trapezium has the following key properties:
- It has one pair of parallel sides and one pair of non-parallel sides.
- The sum of two adjacent angles of a trapezium is 180 degrees.
- The sum of all interior angles of a trapezium is 360 degrees.
- The diagonals of a trapezium bisect each other.
- The length of the mid-segment equals half the sum of the two parallel bases.
What Are the Key Terms Used in Trapezium Geometry?
The key terms in trapezium geometry are: Bases (the two parallel sides, which can be the same or different lengths), Legs (the two non-parallel sides), Height (the perpendicular distance between the two parallel bases), Mid-segment (the line connecting midpoints of both legs), and Isosceles trapezium (a trapezium with equal legs).
Base: The two parallel sides of a trapezium are called bases, regardless of how the trapezium is oriented. They can be of the same or different lengths. The non-parallel sides are called legs.
Height: The maximum perpendicular distance between the two parallel sides of the trapezium is called its height.
Mid-segment: The line segment drawn from the midpoint of one non-parallel side to the midpoint of the other is called the mid-segment. It is parallel to the bases and its length equals the average of the two parallel sides.
Isosceles trapezium: A special type of trapezium in which the two non-parallel sides (legs) are of equal length. It has equal base angles and a line of symmetry.
Area of a Circle: Formula, Methods and ProofsRead →How Do You Calculate the Area of a Trapezium?
The area of a trapezium is Area = (1/2) x h x (a + b), where a and b are the lengths of the two parallel sides and h is the perpendicular height. This formula is derived by dividing the trapezium into a rectangle and two right-angled triangles, then adding their individual areas.
To derive the formula, consider a trapezium with parallel sides of lengths a and b (where a is less than b) and a height h. Place the trapezium with side b as the base.
Draw perpendiculars from the ends of side a to side b so that the trapezium is divided into two right-angled triangles (each with height h and base (b - a) / 2) and one rectangle of length a and height h.
Place the two triangles together (height to height) to form a single triangle with base (b - a) and height h.
Adding the areas of the rectangle and the resulting triangle gives:
Area of trapezium = Area of rectangle + Area of triangle
= (a x h) + (1/2 x (b - a) x h)
= h x (a + 1/2 b - 1/2 a)
= h x (1/2 a + 1/2 b)
Therefore:
Area of trapezium = (1/2) x h x (a + b) = (1/2) x height x (sum of parallel sides)
Area of an Equilateral Triangle: Formula and ExamplesRead →Where Can You Find Trapezium Shapes in Daily Life?
Trapezium shapes appear in many everyday objects and designs. Window and door frames, handbags, pencil boxes, tabletops, and architectural structures often feature trapezoidal forms. In engineering and design drawings, trapezoidal projections are common. Trapezoidal cross-sections are also widely used in civil engineering, such as irrigation canals.
Trapezoid shapes are commonly seen in architectural designs and projection drawings used in engineering.
In daily life, trapezium shapes can be observed in certain types of windows, doors, tabletops, and furniture designs.
Pencil boxes, handbags, and some types of trays also often resemble the shape of a trapezium when viewed from the side.
The trapezoidal channel cross-section is a standard shape in civil engineering for water distribution and irrigation systems due to its structural efficiency.