Question

if the area of a Trapezium is 48 CM square find one of its parallel sides if an other parallel sides is of 12 cm and distance between the parallel sides is 6 CM​

Answer 1

Answer :

›»› The one of it's parallel sides of a trapezium is 4 cm.

Step-by-step explanation :

Given :

• Area of a trapezium = 48 cm².
• Other parallel sides of trapezium = 12 cm.
• Distance between the parallel sides = 6 cm.

To Find :

• One of it's parallel sides of a trapezium = ?

Formula required :

Formula of area of a trapezium to calculate the one of it's parallel sides of a trapezium is given by,

→ Area of trapezium = 1/2 × (a + b) × h.

Here,

• a and b are the parallel sides.
• h is the height of trapezium.

We know that, height is equal to the distance between the parallel sides.

Units,

• The unit of a and b is cm.
• The unit of h is the cm.

Solution :

Let us assume that, the one of it's parallel sides of a trapezium is x cm.

We know that, if we are given with the area of trapezium, other parallel sides of trapezium and distance between the parallel sides, then we have the required formula, that is,

→ Area of trapezium = 1/2 × (a + b) × h.

By using the formula of area of a trapezium to calculate the one of it's parallel sides of a trapezium and substituting all the given values in the formula, we get :

→ 48 = 1/2 × (x + 12) × 6

→ 48 = 1 × (x + 12) × 3

→ 48 = (x + 12) × 3

→ 48/3 = x + 12

→ 16 = x + 12

→ 16 - 12 = x

→ x = 4.

Hence, the one of it's parallel sides of a trapezium is 4 cm.

Answer 2

Answer:

Given :-

• The area of trapezium is 48 cm and the other parallel sides is 12 cm and distance between the parallel sides is 6 cm.

To Find :-

• What is the other parallel sides.

Formula Used :-

✪ Area of trapezium = ½ × Sum of parallel sides × Height ✪

Solution :-

Let, the other side of trapezium be x

Given :

• Area of trapezium = 48 cm
• Other parallel side = 12 cm
• Distance between the parallel sides = 6 cm

According to the question by using the formula we get,

⇒ 48 = ½ × x + 12 × 6

⇒ 48 = ½ × x + 12 × 6

⇒ 48 = x + 12 × 3

⇒ 48/3 = x + 12

⇒ 16 = x + 12

⇒ 16 - 12 = x

⇒ 4 = x

➠ x = 4 cm

∴ The other parallel sides of a trapezium is 4 cm .

Let's Verify :-

↦ 48 = ½ × x + 12 × 6

Put x = 4

↦ 48 = ½ × 4 + 12 × 6

↦ 48 = ½ × 16 × 6

↦ 48 = 8 × 6

↦ 48 = 48

➦ LHS RHS

Hence, Verified ✔