Question

5.

Find the perpendicular distance between two parallel lines of a trapezium whose parallel sides are 30
cm and 24 cm, and area is 405 cm2​

Answer 1

Answer :-

• The perpendicular distance between two parallel lines of a trapezium is 15cm.

Step-by-step explanation:

To Find :-

• The perpendicular distance between two parallel sides of trapezium

Solution:

Given that,

• The parallel sides of trapezium = 30cm and 24cm
• The area of trapezium = 405cm²

As we know that,

Area of trapezium = 1/2 × (sum of all parallel sides) × (distance between them),

Assumption: Let us assume The perpendicular distance between two parallel lines of a trapezium as "h"

=> 1/2 × (sum of all parallel sides) × (distance between them) = Area

=> 1/2 × ( 30 + 24 ) × h = 405

=> 1/2 × 54 × h = 405

=> 1 × 27 × h = 405

=> 27 × h = 405

=> h = 405/27

=> h = 15

Hence,

• The perpendicular distance between two parallel lines of a trapezium is 15cm.

Answer 2

Given :-

• Area of Trapezium = 405cm²
• First Parallel Side = 30cm
• Second Parallel Side = 24cm

To Find :-

• Distance between two parallel Sides of a trapezium.

Solution :-

❍ As we know that Area of Trapezium is given by [ Area of Trapezium = ½ × Height × Sum of Parallel Side ]

Putting the Values :

⟼⠀⠀Area = ½ × Height × ( Sum of Sides )

⟼⠀⠀405 = ½ × Height × ( 30 + 24 )

⟼⠀⠀405 × 2 = Height × ( 30 + 24 )

⟼⠀⠀810 = Height × ( 30 + 24 )

⟼⠀⠀810 = Height × 54

⟼⠀⠀810 / 54 = Height

⟼⠀⠀15cm = Height

________________

Verification :-

⟼⠀⠀Area = ½ × Height × ( Sum of Sides )

⟼⠀⠀Area = ½ × 15 × ( 30 + 24 )

⟼⠀⠀Area = ½ × 15 × 54

⟼⠀⠀Area = 15 × 27

⟼⠀⠀405 = 405

Hence Verified

________________

Thus, Distance between the two parallel Sides of a trapezium is 15cm

________________