Question

The area of a trapezium is 36 cm squared and the perpendicular distance between its parallel sides is 6cm. If the lengths of these parallel sides are x cm and y cm respectively, find the value of x+y.

Answer 1

Working out:

In the question, area of a trapezium is given and also the Perpendicular distance/altitude is given. The sides are also given but in the form of variables.

We have to find the sum of parallel sides of the trapezium, Now we will wonder how can we do that because parallel sides are in given in variable form. It is because :

• Area of trapezium = 1/2 × (Sum of parallel sides of the trapezium) × Perpendicular distance betwe ln the parallel sides..

Now let's plug the given values in the formula,

• Area = 36 cm²
• perpendicular distance = 6 cm
• Sum of parallel sides = x + y

Putting in formula,

⇛ Area = 1/2 × Sum of || sides × altitude

⇛ 36 cm² = 1/2 × (x + y) × 6 cm

⇛ 36 cm² = 3 cm × (x + y)

Flipping it,

⇛ 3 cm × (x + y) = 36 cm²

⇛ x + y = 36 cm² / 3 cm

⇛ x + y = 12 cm

So, the value of x + y:

$\large{ \boxed{ \bf{ \purple{12 \: cm}}}}$

And we are done !!

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Answer 2

Answer:

✡ Question ✡

⬛ The area of a trapezium is 36 cm squared and the perpendicular distance between its parallel sides is 6cm. If the lengths of these parallel sides are x cm and y cm respectively, find the value of x+y.

✡ Given ✡

⬛ The area of a trapezium is 36 cm squared and the perpendicular distance between its parallel sides is 6cm.

⬛ If the lengths of these parallel sides are x cm and y cm respectively.

✡ To Find ✡

⬛ The value of x+y.

✡ Formula Used ✡

✴ Area = $\dfrac{1}{2}$ × Sum of || sides × altitude ✴

✡ Solution ✡

⬛ Area = 36 cm²

⬛ Perpendicular distance = 6 cm

⬛ Sum of parallel sides = x + y

▶ According to the question,

By putting the value we get,

=> 36 cm² = 1/2 × (x + y) × 6 cm

=> 36 cm² = 3 cm × (x + y)

=> 3 cm × (x + y) = 36 cm²

=> x + y = 36 cm² / 3 cm

=> x + y = 12 cm

∴ The value of x + y = $\large \bold{ \underline{ \mathbb{ \blue{12\: cm}}}}$

Step-by-step explanation:

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