Question

The area of trapezium is 480 square cm. If one of parallel side is 24cm longer than the other and the distance between them is 15cm, then find the length of both parallel sides.

Answer 1

GIVEN :-

• Area of trapezium is 480cm².
• One of the parallel side is 24cm longer than other side.
• Distance between these two parallel sides is 15cm.

TO FIND :-

• The two parallel sides of trapezium.

TO KNOW :-

$\\ \bigstar\boxed{ \sf \: area \: of \: trapezium = \left( \dfrac{sum \: of \: parallel \: sides}{2} \right) \times height}$

SOLUTION :-

→ Let one of the parallel side be 'x'cm.

Other side is 24cm longer.

→ Other side will be 'x+24' cm.

→ Height is 15cm.

→ Area is 480cm².

Putting values in formula,

$\\ \implies\sf \: 480 = \dfrac{x + x + 24}{2} \times 15 \\ \\ \\ \implies\sf \: 480 = \dfrac{2x + 24}{2} \times 15 \\ \\ \\ \implies\sf \: \dfrac{480}{15} = \dfrac{2x + 24}{2} \\ \\ \\ \implies \sf \: 32 = \dfrac{2x + 24}{2} \\ \\ \\ \implies \sf \: 64 = 2x + 24 \\ \\ \\ \implies\sf \: 64 - 24 = 2x \\ \\ \\ \implies\sf \: 40 = 2x \\ \\ \\ \implies \boxed{ \bf \:x = 20 }$

Hence Parallel sides are :-

• x = 20cm
• x + 24 = 20+24 = 44cm

Hence , parallel sides are 20cm and 44cm.

MORE TO KNOW :-

★ Area of square = side²

★ Area of rectangle = l × b

★ Area of circle = πr²

★ Area of hemisphere = πr²/2

★ Area of parallelogram = l × h

Answer 2

Given :-

Area of trapezium = 480cm²

Height of trapezium = 15cm

One of parallel side is 24cm longer than the other side.

To find:-

Length of other side.

Using formula:-

$\bf Area\: of\: trapezium\: = \dfrac{1}{2}\times h \times (sum\:of\:parallel\: sides)$

Solution :-

Area of trapezium = 480cm²

Height of trapezium = 15cm

Let one parallel side be 'x'

Other side = x + 24

$\rm Area\: of\: trapezium\: = \dfrac{1}{2}\times h \times (sum\:of\:parallel\: sides)$

$\implies\rm 480 = \dfrac{1}{2}\times 15 \times (x + x + 24)$

$\implies\rm 480 = \dfrac{1}{2}\times 15 \times (2x+ 24)$

$\implies\rm \dfrac{480}{15}= \dfrac{1}{2} \times (2x+ 24)$

$\implies\rm \cancel \dfrac{480}{15}= \dfrac{1}{2} \times (2x+ 24)$

$\implies\rm 32 = \dfrac{1}{2} \times (2x+ 24)$

$\implies\rm 32 \times 2 = 2x+ 24$

$\implies\rm 64 = 2x+ 24$

$\implies\rm 64 -24 = 2x$

$\implies\rm 40 = 2x$

$\implies\rm \dfrac{40}{2} = x$

$\implies\rm \cancel \dfrac{40}{2} = x$

$\implies \rm 20 = x$

Therefore,

One parallel side of the trapezium = 20cm

Other side of the trapezium = x + 24

= 20+24 = 44cm