Question

the area of a Trapezium is 1824 CM square. if the length of its parallel sides are 55 cm and 59 cm find the distance between them​

Answer 1

Answer:

Length of parallel sides are 55 cm and 35 cm.

Sum of parallel side's = ( 55 + 35 ) cm = 90 cm.

Let distance between the two parallel sides = X cm.

Area of trapezium = 1080 cm².

1/2 × ( Sum of parallel sides ) × ( Distance between them ) = 1080

1/2 × 90 × X = 1080

90X = 2160

X = 2160/90

X = 24 cm.

Hence,

Distance between parallel side's = X cm = 24 cm.

Step-by-step explanation:

Answer 2

Given :-

• The Area of Trapezium = 1824cm²
• First Parallel Side = 55cm
• Second Parallel Side = 59cm

To Find :-

• Distance between the Sides (Height)

Solution :-

❏ As we know that, Area of Trapezium is given [ Area = ½ × Height × ( S1 + S2 ) ] where S1 and S2 stands for Parallel Side 1 and Parallel Side 2 respectively.

Putting the Values :

⟾⠀⠀Area = ½ × Height × ( S1 + S2 )

⟾⠀⠀1824 = ½ × Height × ( 55 + 59 )

⟾⠀⠀1824 × 2 = Height × ( 55 + 59 )

⟾⠀⠀3648 = Height × ( 55 + 59 )

⟾⠀⠀3648 = Height × 114

⟾⠀⠀3648 / 114 = Height

⟾⠀⠀32cm = Height

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Verification :

⟼⠀⠀Area = ½ × Height × ( S1 + S2 )

⟼⠀⠀Area = ½ × 32 × ( 55 + 59 )

⟼⠀⠀Area = ½ × 32 × 114

⟼⠀⠀Area = 32 × 57

⟼⠀⠀1824 = 1824

Hence Verified

Thus, Height of the Trapezium = 32cm

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