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
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Answer 1

Answer :-

• The length of parallel sides of trapezium are 15cm and 11cm.

Step-by-step explanation:

To Find :-

• The two parallel sides of trapezium.

Solution:

Given that,

• The area of trapezium = 143cm²
• The height of the trapezium = 11cm
• One parallel side is longer than the other parallel side by 4cm.

Assumption: Let us assume shorter parallel side of trapezium as "(x) cm" and the longer parallel side of trapezium as "(x+4) cm"

We know,

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

Where,

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

Therefore,

$\bf{\mapsto \: \dfrac{1}{2} \times (a + b) \times h = Area} \\ \\ \\ \\ \bf{\mapsto \: \dfrac{1}{2} \times (x) + (x + 4) \times 11 = 143} \\ \\ \\ \\ \bf{\mapsto \: \dfrac{1}{2} \times (x + x + 4) \times 11 = 143} \\ \\ \\ \\ \bf{\mapsto \: \dfrac{1}{2} \times (2x + 4) \times 11 = 143}$

$\bf{\mapsto \: 1 \times (2x + 4) \times 11 = 143 \times 2} \\ \\ \\ \\ \bf{\mapsto \: 1 \times (2x + 4) \times 11 = 286} \\ \\ \\ \bf{\mapsto \: 1 \times (2x + 4) = \dfrac{286}{11}}$

$\bf{\mapsto \: 1 \times (2x + 4) = \cancel{\dfrac{286}{11}}} \\ \\ \\ \\ \bf{\mapsto \: 1 \times (2x + 4) = 26} \\ \\ \\ \\ \bf{\mapsto \: (2x + 4) = 26} \\ \\ \\ \\ \bf{\mapsto \: 2x = 26 - 4} \\ \\ \\ \\ \bf{\mapsto \: 2x = 22} \\ \\ \\ \\ \bf{\mapsto \: x = \dfrac{22}{2}} \\ \\ \\ \\ \bf{\mapsto \: x = \cancel{\dfrac{22}{2}}} \\ \\ \\ \\ \bf{\mapsto \: \boxed{ \bf{x = 11}}}$

Hence, The value of x is 11. now, the length of each parallel sides are :-

The length of a parallel side which is longer than other by 4cm. [(x+4) cm]

$\bf{\mapsto \: ( x + 4 ) cm} \\ \\ \bf{\mapsto \: ( 11 + 4 ) cm} \\ \\ \bf{\mapsto \: \boxed{ \bf{\red{15cm}}}}$

The length of parallel side which is shorter than the other parallel side. [(x) cm]

$\bf{\mapsto \: ( x )cm} \\ \\ \bf{\mapsto \: \boxed{ \bf{\red{11cm}}}}$

∴ The length of parallel sides of trapezium are 15cm and 11cm.

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 ⟼ 143 cm²

• Height of the trapezium ⟼ 11 cm

It is also given that, one of the parallel sides is longer than the other parallel side by 4 cm.

To Find:

• 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 of the trapezium

Solution:

Let,

• the shorter parallel side of the trapezium, a ⟼ x cm

• the longer parallel side of the trapezium, b ⟼ ( x + 4 ) cm

Now,

Finding the value of x:

Using the area of the trapezium Formula,

Area of the trapezium = 143 cm²

➞ 1/2 × ( a + b ) × h = 143

➞ 1/2 × ( x + x + 4 ) × 11 = 143

➞ 1/2 × ( 2x + 4 ) × 11 = 143

➞ 1 × ( 2x + 4 ) × 11 = 143 × 2

➞ 2x + 4 × 11 = 143 × 2

➞ 2x + 4 × 11 = 286

➞ 2x + 4 = 286/11

➞ 2x + 4 = 26

➞ 2x = 26 - 4

➞ 2x = 22

➞ x = 22/2

➞ x = 11

Hence, the value of x is 11

Finding the Shorter parallel side:

The shorter parallel side , a ⟼ x cm

⟼ 11 cm

Finding the Longer parallel side:

The longer parallel side , b ⟼ ( x + 4 ) cm

⟼ ( 11 + 4 ) cm

⟼ 15 cm

∴ The two parallel sides of the trapezium are 11cm and 15cm.

Happy Learning!!