Question

If the area of a trapezium is 56 sq. cm and one of its parallel sides is 6 cm, find the other parallel side if its altitude is 8 cm.​

Answer 1

S O L U T I O N :

Given :

If the area of a trapezium is 56 cm² & one it's parallel sides is 6 cm & it's altitude is 8 cm.

Explanation :

Let the other parallel side be x.

As we know that formula of the area of trapezium:

• Area = 1/2 ×(sum of base) × height

According to the question :

➝ Area of trapezium = 1/2(sum of base) × height

➝ 56 = 1/2 × (6 + x) × 8

➝ 56 = 1/2 × 48 + 8x

➝ 56 × 2 = 48 + 8x

➝ 112 = 48 + 8x

➝ 8x = 112 - 48

➝ 8x = 64

➝ x = 64/8

➝ x = 8 cm

Thus,

The other parallel side will be 8 cm .

Answer 2

Answer:

Given :-

• Area of trapezium = 56 cm².
• One parallel side = 6 cm
• Altitude = 8 cm

To Find :-

Other parallel side

Solution :-

Let us assume the other parallel side as x

Now,

As we know that

$\bf Area = \frac{1}{2} (sum \: of \: parallel \: side) \times altitude$

$\sf \implies \: 56 = \dfrac{1}{2} \times (x + 6) \times 8$

$\sf \implies \: 56 = \dfrac{1}{2} \times 48 + 8x$

$\sf \implies 56 \times 2 = 48 + 8x$

$\sf \ \implies112 = 48 + 8x$

$\sf \implies \: 112 - 48 = 8x$

$\sf \implies \: 64 = 8x$

$\sf \implies \: \dfrac{64}{8} = x$

$\sf \implies \: 8 = x$

HENCE :-

The other parallel side is 8 cm.