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Home >> Trapezium >> Area of Trapezium >>

## Area of Trapezium

 Area of Trapezium

 Before you study, how to find area of trapezium, you are advised to read: What are Parallel Lines ? How to find Area of Triangle ? How to find area of Rectangle ? Formula for calculating Area of Trapezium: Area of Trapezium = Height ( Σ of || lines ) / 2 Also, note that area of trapezium is always in unit2 e.g. cm2 or m2 etc….. Now, let's understand how formula for area of trapezium is obtained: Observe the following diagram: Above diagram represent Trapezium ABCD. Let's draw a line segment DE parallel to side AB (as shown below) You can observe that here we got a rectangle ABCD and a triangle DEC Now, recall formula for area of Rectangle and Area of Triangle & apply as shown below: Area of Rectangle ABCD = Length X Breadth Since length = AD and Breadth = DE, we get: Area of Rectangle ABCD = AD X DE ……………………..(statement 1) Area of Triangle DEC = 1/2 (Base X Height) Since Base = EC and height = DE, we get: Area of Triangle DEC = 1/2 (EC X DE) Now, Area of Trapezium is equal to area of rectangle ABCD and area of triangle DEC; as shown below: So we get: Area of Trapezium ABCD = Area of Rectangle ABCD + Area of Triangle DEC Put the values from above statement 1 & 2 and we get: = [ AD X DE ] + [ 1/2 ( EC / DE ) ] Take DE common and we get: = DE [ AD + 1/2 EC ] Balance the term in the bracket and we get: = DE [ 2AD + EC ] / 2 Or we can write it as: = DE [ AD + AD + EC ] / 2 Since AD = BE (opposite sides of rectangle are equal), so we get: = DE [ AD + BE + EC ] / 2 See the diagram again, BE + EC = BC, so we get: = DE [ AD + BC ] / 2 Now DE = Height , AD and BC are parallel lines, so we get required formula of trapezium: Height ( Σ of || lines ) / 2 Let's use the formula to following example: Example : Find the area of following Trapezium: Solution: In the given diagram: PQ and SR are parallel line of trapezium PQRS PQ = 5 cm SR = 3 cm TR is the height of trapezium PQRS TR = 4 cm Apply the formula: Area of Trapezium = Height ( Σ of || lines ) / 2 Or we can write its as: = TR (PQ + SR) / 2 Put values of TR, PQ and SR from the above and we get: = 4 ( 5 + 3 ) / 2 Solve brackets and we get: = 4 (8) / 2 Solve division expression and we get: = 4 (4) Solve multiplication expression and we get: = 16 Hence, area of trapezium PQRS is 16 cm2

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