- Books Name
- class 8 th Mathematics Book
- CBSE Class 8
A trapezium is a quadrilateral with one pair of opposite side parallel.
For the trapezium ABCD, the following will be true:
- AB||DC,where AB and DC are parallel sides
- CE⊥AB, where CE is perpendicular to AB
- DF⊥AB, where DF is perpendicular to AB
- CE=DF=h, where h is the height of the trapezium
Area, perimeter of trapezium
Area of trapezium: To obtain the area of a trapezium, multiply the sum of the bases by the height and then divide by 2.
The area of a trapezium is computed with the following formula:
Area of trapezium = 12×(a+b)×(h) square units.
(where a and b is bases (parallel sides) and h is leg or height (between the non-parallel sides)).
Area of the trapezium ABCD:
Proof: Area of a trapezium ABCD.
Area of trapezium ABCD = 12(AB+DC)×(h) squareunits.
= area of triangle (DEA) + area of rectangle (DEFC) + area of triangle (CFB)
= 12×AE×DE + DE×EF + 12×FB×CF
= 12×AE×h + h×EF + 12×FB×h
= 12×(sum of parallel side) ×(height) square units.
Therefore, Area of trapezium ABCD= 12×(a+b)×(h) or
Perimeter of trapezium: The Perimeter is the sum of all side lengths.
The perimeter of a trapezium is computed with the following formula:
Perimeter of trapezium = a+b+c+d (where a, b are denoted as bases (parallel sides) and c, d are denoted as legs (non-parallel sides)).
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