Question

the area of trapezium is 340cm^2 length of parallel side is 24 and 10 cm find distance between parallel side​

Answer 1

Given :

• Area of trapezium = 340 cm²
• Length of parallel side = 24 cm and 10 cm

To find :

• Distance between the parallel sides

Knowledge required :-

• Formula of area of trapezium :-

⠀⠀⠀Area = 1/2 × Sum of parallel sides × Distance between the parallel sides

Solution :

Let the distance between the parallel sides be h.

⠀⠀⠀

⠀⠀⠀⇒ 340 = 1/2 × (24 + 10) × h

⠀⠀⠀⇒ 340 = 1/2 × 34 × h

⠀⠀⠀⇒ 340 = 17 × h

⠀⠀⠀⇒ 340/17 = h

⠀⠀⠀⇒ 20 = h

∴ The distance between the parallel sides = 20 cm

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⠀⠀⠀⠀⠀⠀⠀⠀⠀Verification :

Substitute the value of h in 340 = 1/2 × (24 + 10) × h

Taking Rhs,

⠀⠀⠀⇒ 1/2 × (24 + 10) × h

⠀⠀⠀⇒ 1/2 × 34 × 20

⠀⠀⠀⇒ 17 × 20

⠀⠀⠀⇒ 340

Rhs = 340

Lhs = 340

Lhs = Rhs

Hence, verified.

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⠀⠀⠀⠀⠀Know MorE

More about trapezium :-

• Trapezium has 4 sides, 4 angles.
• Sum of the 4 angles of trapezium = 360°
• Trapezium has two parallel and two non - parallel sides.
• Perimeter of trapezium = Sum of all its sides.

Answer 2

Given :-

• Area of Trapezium = 340cm²
• First Parallel Side = 24cm
• Second Parallel Side = 10cm

To Find :-

• Height of Trapezium

Solution :-

❏ As we know that, Area of Trapezium is given by [ Area = ½ × Height × ( Sum of Parallel Side )

Putting the Values :

➞ Area = ½ × Height × (Sum of Parallel Side)

➞ 340 = ½ × Height × ( 24 + 10 )

➞ 340 × 2 = Height × ( 24 + 10 )

➞ 680 = Height × ( 24 + 10 )

➞ 680 = Height × 34

➞ 680 / 34 = Height

➞ 20cm = Height

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Verification :

⟾ Area = ½ × Height × (Sum of Parallel Side)

⟾ Area = ½ × 20 × ( 24 + 10 )

⟾ Area = 10 × ( 24 + 10 )

⟾ Area = 10 × 34

⟾ 340 = 340

Hence Verified

Thus Height of Trapezium is 20cm

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