Question

the lenght of one of the parallel sides of a trapezium is 80 cm and the distance between the two parallel sides 4 cm .find the lenght of the other side if the area of the trapezium is 256 cm²​

Answer 1

Answer :

Correct Question :-

The Length of one of the parallel sides of a trapezium is 80 cm and the distance between the parallel sides is 4 cm. Find the length of other parallel side , if the area of the Trapezium is 256 cm ².

To Find :-

The length of other parallel side.

Given :-

⠀⠀⠀$\bigstar\:$Length of one of the parallel side = 80 cm

⠀⠀⠀$\bigstar\:$Distance between the parallel sides = 4 cm.

⠀⠀⠀$\bigstar\:$Area of the Trapezium = 256 cm².

We know :-

⠀⠀⠀⠀⠀⠀Area of an Trapezium :-

$\underline{\boxed{\bf{A = \dfrac{1}{2} \times (p_{1} + p_{2}) \times h}}}$

Where :-

• A = Area of the Trapezium

• $p_{1}$ = Parallel side

• $p_{2}$ = Parallel side

• h = Distance between the parallel sides.

Solution :-

Let the other parallel side of the Trapezium be x m.

So, using the formula for area of a Trapezium and substituting the values in it, we get :-

$:\implies \bf{A = \dfrac{1}{2} \times (p_{1} + p_{2}) \times h} \\ \\ \\ :\implies \bf{256 = \dfrac{1}{2} \times (80 + x) \times 4} \\ \\ \\ :\implies \bf{256 \times 2 = (80 + x) \times 4} \\ \\ \\ :\implies \bf{512 = (80 + x) \times 4} \\ \\ \\ :\implies \bf{512 = 320 + 4x} \\ \\ \\ :\implies \bf{512 - 320 = 4x} \\ \\ \\ :\implies \bf{192 = 4x} \\ \\ \\ :\implies \bf{\dfrac{192}{4} = x} \\ \\ \\ :\implies \bf{48 = x} \\ \\ \\ \therefore \purple{\bf{Length\:of\:other\:parallel\:side = 48 cm}}$

Hence, the length of other parallel side is 48 cm.

Answer 2

Given,

• Length of one parallel side of trapezium = 80 cm
• Distance between two parallel sides of trapezium = 4 cm
• Area of trapezium = 256 cm²

We have,

• To figure out measure of the other side of trapezium

We know,

• Formula for area of trapezium

$\orange \implies \green{\dfrac{1}{2} \bigg\{ \text{Sum of parallel sides} \bigg\} \times \text{Distance between parallel sides}} \\ \small \orange \implies \purple{\dfrac{1}{2} \bigg\{ \text{Sum of parallel sides } \bigg\} \times \text{Perpendicular Height between parallel sides}}$

Now, Putting the known values in the formula,

$\to \dfrac{1}{2} \bigg\{ 80 + \rm unknown \: parallel \: side\bigg\} \times 4 = 256 \\ \\ \to \dfrac{1}{2} \bigg\{ 80 + \rm unknown \: parallel \: side\bigg\} = \dfrac{256}{4} \\ \\ \to \dfrac{1}{2} \bigg\{ 80 + \rm unknown \: parallel \: side\bigg\} = 64 \\ \\ \to \bigg\{ 80 + \rm unknown \: parallel \: side\bigg\} = \frac{64}{ \frac{1}{2} } \\ \\ \to \bigg\{ 80 + \rm unknown \: parallel \: side\bigg\} = 88 \\ \to\big\{\rm unknown \: parallel \: side\big\} = 128 - 80 \\ \to\big\{\rm unknown \: parallel \: side\big\} = 48 \: cm$

Thus,

• A trapezium with area of 256 cm², whose one of the parallel sides measure 80 cm and distance between the parallel sides is 4 cm, will have another parallel side of 48 cm