Mensuration - Trapezium | Formulae & Concepts | Aptitude Tricks in Tamil | Quantitative Aptitude
In this video we are going to learn formulae and concepts of Trapezium with 5 different questions in Mensuration Topic.
Mensuration is the branch of mathematics that studies the measurement of geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc
The trapezium is a quadrilateral with two parallel sides. The parallel sides of a trapezium are called bases and the non-parallel sides of a trapezium are called legs. It is also called a trapezoid. Sometimes the parallelogram is also called a trapezoid with two parallel sides.
Types of Trapezium
The trapezium is further categorised into three different types, namely
Isosceles trapezium – The legs or the non-parallel sides of the trapezium are of equal length
Scalene Trapezium – A trapezium with all the sides and angles of different measures
Right Trapezium – A right trapezium has at least two right angles
Properties of Trapezium
Some important properties of a trapezium are as follows:
In trapezium, exactly one pair of opposite sides are parallel
The diagonals intersect each other
The non-parallel sides in the trapezium are unequal except in isosceles trapezium
The line that joins the mid-points of the non-parallel sides is always parallel to the bases or parallel sides which is equal to half of the sum of parallel sides
Mid-segment = (AB+ CD)/2
Where AB and CD are the parallel sides or bases
In isosceles trapezium, the legs or non-parallel sides are congruent
The sum of the interior angles of the trapezium is equal to 360 degrees. i.e., ∠A + ∠B + ∠C + ∠D = 360°
The sum of the two adjacent angles is equal to 180°. This means that the two adjacent angles are supplementary.
Area of Trapezium:
The area of a trapezium can be found by taking the average of the two bases of a trapezium and multiply by its altitude. So, the area of trapezium formula is given as:
Area of a Trapezium, A = h(a+b)/2 square units.
Where,
“a” and “b” are the bases
“h” is the altitude or height.
Perimeter of Trapezium
The perimeter of a trapezium is found by adding all the sides. Therefore, the perimeter of a trapezium formula is given as
The perimeter of Trapezium, P = a + b+ c + d units
Where,
“a, b, c, d” are the sides of the trapezium
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