Question

The area of a trapezium is 1,586 cm² and sum of parallel sides is 122 cm. Find the
distance between two parallel sides. help me with full Process ​

Answer 1

Answer :-

• The distance between two parallel sides of trapezium is 26cm.

Step-by-step explanation:

To Find :-

• The distance between two parallel sides of trapezium

Solution:

Given that,

• The area of trapezium = 1586cm²
• The sum of two parallel sides of trapezium = 122cm

We know,

$\bigstar \: \: \boxed{\bf{Area \: of \: trapezium = \dfrac{1}{2} \times (a + b) \times h}}$

Where,

• a and b are two parallel sides of trapezium.
• h is the distance between two parallel sides of trapezium.

Therefore,

$\bf{\mapsto \: \dfrac{1}{2} \times (a + b) \times h = Area} \\ \\ \\ \\ \bf{\mapsto \: \dfrac{1}{2} \times 122 \times h = 1586} \\ \\ \\ \\ \bf{\mapsto \: \dfrac{1}{ \cancel{2}} \times \cancel{122} \times h = 1586} \\ \\ \\ \\ \bf{\mapsto \: 1 \times 61 \times h = 1586}\\ \\ \\ \\ \bf{\mapsto \: 61 \times h = 1586} \\ \\ \\ \\ \bf{\mapsto \: h = \dfrac{1586}{61}}\\ \\ \\ \\ \bf{\mapsto \: h = \cancel{\dfrac{1586}{61}}} \\ \\ \\ \\ \bf{\mapsto \: \boxed{ \bf{\red{h = 26}}}}$

Hence, The distance between two parallel sides is 26cm.

Answer 2

Question:

The area of the trapezium is 143cm² and it's height is 11cm if one of the parallel sides is longer than the other by 4cm , find two parallel sides.

Given:

• Area of the trapezium ⟼ 1586 cm²

• Sum of the two parallel side of the trapezium, a and b ⟼ 122 cm

To Find:

• The distance between the two parallel sides.

Formula Used:

• Area of the trapezium = 1/2 × ( a + b ) × h

where,

• 'a' and 'b' is the parallel sides of the trapezium

• 'h' is the height or distance between the trapezium

Solution:

Finding the value of h,

Using the area of the trapezium Formula,

Area of the trapezium = 1586 cm²

➞ 1/2 × ( a + b ) × h = 1586

➞ 1/2 × ( 122 ) × h = 1586

➞ 1 × 61 × h = 1586

➞ 61 × h = 1586

➞ h = 1586/61

➞ h = 26 cm

Hence, the value of h is 26 cm

∴ The distance between the two parallel sides , h is 26 cm

Happy Learning!!