Question

The two parallel sides and the height between them are in the ratio
3:7:4. If the area of the trapezium is 180 cm”. Determine its height​

Answer 1

Given:

✰ The two parallel sides and the height between them are in the ratio 3:7:4.

✰ The area of the trapezium = 180 cm²

To find:

✠ The height of the trapezium.

Solution:

Lets understand the concept first! First we will assume that the two parallel sides and the height between them are 3x, 7x and 4x respectively. Then, we will use formula of area of trapezium to calculate the value of x. We will substitute the value of its two parallel sides, height and the area of trapezium. Then find out the value of x. After that we will substitute the value of x in the height of the trapezium to find out the actual height of the trapezium.

Let the two parallel sides of the trapezium be 3x and 7x respectively, and

the height of the trapezium be 4x.

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

Where,

• a and b are the parallel sides of the trapezium.
• h is the height of the trapezium that is the distance between its parallel sides.

Putting the values in the formula, we have:

➤ 180 = 1/2 × ( 3x + 7x ) × 4x

➤ 180 = 1/2 × 10x × 4x

➤ 180 = 1/2 × 40x²

➤ 40x² = 180 × 2

➤ 40x² = 360

➤ x² = 360/40

➤ x² = 9

➤ x = √9

➤ x = 3

Now, Substitute the value of x in height of trapezium.

➛ The height of the trapezium = 4x

➛ The height of the trapezium = 4 × 3

➛ The height of the trapezium = 12 cm

∴ The height of the trapezium = 12 cm

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Answer 2

Given :

• The two parallel sides and the height between them are in the ratio 3:7:4.
• Area of Trapezium = 180cm²

To Find :

• Height of Trapezium

Solution :

⟶ Let 1st Parallel Side be 3x

⟶ Let 2nd Parallel Side be 7x

⟶ Let height of Trapezium be 4x

⠀⠀⠀

✰ As we know that, Area of Trapezium is given by ½ × height × (sum of parallel sides) . So Simply we will put the given values in the Formula to find height of the Trapezium.

⠀

According to the Question :

⟹ Area = ½ × h × (S1 + S2)

⟹ 180 = ½ × 4x × (3x + 7x)

⟹ 180 = ½ × 4x × 10x

⟹ 180 = 2x × 10x

⟹ 180 = 20x²

⟹ 180 / 20 = x²

⟹ 9 = x²

⟹ √9 = x

⟹ 3 = x

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Verification :

➟ Area = ½ × h × (S1 + S2)

➟ Area = ½ × 4x × (3x + 7x)

➟ Area = ½ × 4x × 10x

➟ Area = ½ × 4 × 3 × 10 × 3

➟ Area = ½ × 12 × 30

➟ Area = ½ × 360

➟ 180 = 180

Hence Verified

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Therefore :

• Height = 4x = 4 × 3 = 12cm

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