Question

*If the area of a trapezium is 25 sq.cm. and length of the parallel sides are 8 cm and 12 cm respectively ,what is the distance between the parallel sides?*

1️⃣ 2.5 cm
2️⃣ 5 cm
3️⃣ 1.25 cm
4️⃣ can't say​

Answer 1

Given :

• Area of Trapezium is 25 cm² .
• Length of the parallel sides are 8 cm and 12 cm .

To Find :

• Distance between the parallel sides / Height of Trapezium .

Solution :

$\longmapsto\tt{Parallel\:Sides=8\:cm\:and\:12\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}$

Putting Values :

$\longmapsto\tt{25=\dfrac{1}{2}\times{(8+12)}\times{h}}$

$\longmapsto\tt{25=\dfrac{1}{{\cancel{2}}}\times{{\cancel{20}}}\times{h}}$

$\longmapsto\tt{25=10\:h}$

$\longmapsto\tt{h=\dfrac{25}{10}}$

$\longmapsto\tt\bf{h=2.5\:cm}$

So , The Distance between the parallel sides is 2.5 cm .

Option 1) 2.5 cm is Correct .

VERIFICATION :

$\longmapsto\tt{25=\dfrac{1}{{\cancel{2}}}\times{{\cancel{20}}}\times{2.5}}$

$\longmapsto\tt{25=10\times{2.5}}$

$\longmapsto\tt\bf{25=25}$

HENCE VERIFIED

Answer 2

Given :-

Area = 25 cm²

Length of parallel sides = 8 and 12 cm

To Find :-

Distance between them

Solution :-

We know that

${\boxed{\red{\pmb{\underline{\frak{Area = \dfrac{1}{2}\times(a + b)h}}}}}}$

According to the question

25 = ½ × (8 + 12) h

25 × 2 = (8 + 12)h

50 = 20h

50/20 = h

2.5 = h

Hence, height is 2.5 cm