Question

The area of the trapezium
is 176cm2. The distance
between parallel sides is 8cm
and one of the parallel side is
34cm. The other side is​

Answer 1

Given :

• Area of Trapezium is 176 cm ² .
• Distance between its parallel sides is 8 cm .
• One parallel side of trapezium is 34 cm .

To Find :

• Other Parallel Side of Trapezium .

Solution :

$\longmapsto\tt{Let\:other\:parallel\:side\:be=x\:cm}$

$\longmapsto\tt{Height=8\:cm}$

Using Formula :

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

Putting Values :

$\longmapsto\tt{176=\dfrac{1}{{\not{2}}}\times{(34+x)}\times{{\not{8}}}}$

$\longmapsto\tt{176=(34+x)\times{4}}$

$\longmapsto\tt{176=136\times{4x}}$

$\longmapsto\tt{176-136=4x}$

$\longmapsto\tt{40=4x}$

$\longmapsto\tt{x=\cancel\dfrac{40}{4}}$

$\longmapsto\tt\bf{x=10\:cm}$

Value of x is 10 cm .

Therefore :

$\longmapsto\tt{Other\:parallel\:side=x}$

$\longmapsto\tt\bf{10\:cm}$

___________________

VERIFICATION :

$\longmapsto\tt{176=\dfrac{1}{{\not{2}}}\times{(34+10)}\times{{\not{8}}}}$

$\longmapsto\tt{176=44\times{4}}$

$\longmapsto\tt\bf{176=176}$

HENCE VERIFIED

Answer 2

Answer:

• Area of trapezium = 176 cm²
• Distance b/w parallel sides = 8 cm
• One of parallel side = 34 cm

$\setlength{\unitlength}{1.2cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(10.2,0.6){\sf34 cm}\put(10.4,3.17){\sf?}\put(8,1){\line(1,0){5}}\put(12,1){\line(0,2){2}}\put(9,3){\line(3,0){3}}\put(11.2,1.8){\sf8 cm}\qbezier(13,1)(12.5,2)(12,3)\qbezier(8,1)(8.5,2)(9,3)\end{picture}$

⠀

Let another parallel side be n

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Area=\dfrac{1}{2} \times (Sum \:of \:parallel \:sides) \times Height\\\\\\:\implies\sf 176 = \dfrac{1}{2} \times (34 + n) \times 8\\\\\\:\implies\sf 176 = (34 + n) \times 4\\\\\\:\implies\sf \dfrac{176}{4} = (34 + n)\\\\\\:\implies\sf 44 = 34 + n\\\\\\:\implies\sf 44 - 34 = n\\\\\\:\implies\sf n = 10 \:cm$

⠀

$\therefore\:\underline{\textsf{Hence, another parallel side is \textbf{10 cm}}}.$