Question

The area of a trapezium is 34 sq. cm and length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side​

Answer 1

Given :

⬤ Area of Trapezium is 34 cm² .

⬤ Length of One of the Parallel Sides is 10 cm .

⬤ Height of Trapezium is 4 cm .

To Find :

⬤ Length of Other Parallel Side of Trapezium .

Formula Used :

$\bf[\:{Area \: of \: Trapezium = \dfrac{1}{2} \times{(Sum \: of \: Parallel \: Sides)} \times{h}}\:]$

• h = height

Solution :

Let :

• Other Parallel Side be = x .

According to the Formula :-

34 = 1/2 × (Sum of Parallel Sides) × h

34 = 1/2 × (10 + x) × 4

34 = (10 + x) × 2

34/2 = 10 + x

17 = 10 + x

17 - 10 = x

7 = x

Therefore , The Length of Other Parallel Side of Trapezium (x) is 7 .

Check :

34 = 1/2 × (10 + x) × 4

34 = 1/2 × (10 + 7) × 4

34 = (10 + 7) × h

34 = 17 × 2

34 = 34

Hence Checked .

Answer 2

• Length of other parallel side is 7 cm.

Step-by-step explanation:

Given:-

• Area of trapezium is 34 cm².
• Length of one parallel side is 10 cm.
• Height of trapezium is 4 cm.

To find:-

• Length of other parallel side.

Solution:-

Let, Other parallel side of trapezium be x.

We know,

Area of trapezium = (Sum of parallel sides)/2 × height

Put area, height and parallel sides in formula

$\longrightarrow$ 34 = (10 + x)/2 × 4

$\longrightarrow$ 34 × 2 = (10 + x) × 4

$\longrightarrow$ 68 = 40 + 4x

$\longrightarrow$ 68 - 40 = 4x

$\longrightarrow$ 28 = 4x

$\longrightarrow$ x = 28/4

$\longrightarrow$ x = 7

Verification:-

$\longrightarrow$ 34 = (10 + x)/2 × 4

• Put x = 7

$\longrightarrow$ 34 = (10 + 7)/2 × 4

$\longrightarrow$ 34 = (17)/2 × 4

$\longrightarrow$ 34 = 8.5 × 4

$\longrightarrow$ 34 = 34

$\boxed{\sf Hence \: Verified.}$

We take other side of trapezium be x.

Therefore,

Length of other parallel side is 7 cm.