Question

The area of the trapezium is 180cm² and it's height is 9cm. If one of the parallel side is longer than the other by 6cm,find the two parallel side

Answer 1

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Answer 2

Given :-

• Shape = Trapezium
• Area of the Trapezium = 180cm²
• Height of the Trapezium = 9cm
• One of the Parallel Side is longer than the other by 6cm

To Find :-

• The Two Parallel Sides of the Trapezium.

Solution :-

➟ Let the First Side be x cm

➟ Then the Second Side will be x + 6 cm

According to the Question :

➞ Area = ½ × Height × Sum of Parallel Sides

➞ 180 = ½ × 9 × ( x + x + 6 )

➞ 180 / 9 = ½ × 2x + 6

➞ 20 = ½ × 2x + 6

➞ 20 × 2 = 2x + 6

➞ 40 = 2x + 6

➞ 40 - 6 = 2x

➞ 34 = 2x

➞ 34 / 2 = x

➞ 17cm = x

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Therefore :-

• First Side = x = 17cm
• Second Side = x + 6 = 17 + 6 = 23cm

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Verification :-

⟾ ⠀⠀Area = ½ × Height × Sum of Sides

⟾ ⠀⠀Area = ½ × 9 × ( 17 + 23 )

⟾ ⠀⠀Area = ½ × 9 × 40

⟾ ⠀⠀Area = 9 × 20

⟾ ⠀⠀180 = 180

Hence Verified

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