Question

the area of trapezium is 128 cm² and it's altitude is 4cm , find the sum of parallel sides ​

Answer 1

Step-by-step explanation:

answer for this question is 64 cm

Answer 2

Answer:

• Area of trapezium = 128 cm²
• Altitude = 4 cm
• Sum of parallel sides = ?

Let the parallel sides be m and n respectively.

$\setlength{\unitlength}{1.2cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(10.3,0.6){\sf{n}}\put(10.4,3.17){\sf{m}}\put(8,1){\line(1,0){5}}\put(12,1){\line(0,2){2}}\put(9,3){\line(3,0){3}}\put(11,1.8){\sf4 cm}\qbezier(13,1)(12.5,2)(12,3)\qbezier(8,1)(8.5,2)(9,3)\end{picture}$

⠀

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

$:\implies\sf Area=\dfrac{1}{2} \times (Sum \:of \:parallel \:sides) \times Altitude\\\\\\:\implies\sf 128 \:{cm}^{2} = \dfrac{1}{2} \times (m + n) \times 4 \:cm\\\\\\:\implies\sf 128 \:{cm}^{2} = (m + n) \times 2 \:cm\\\\\\:\implies\sf \dfrac{128 \:cm^{2} }{2 \:cm} = (m + n)\\\\\\:\implies\sf (m + n) = 64 \:cm$

⠀

$\therefore\:\underline{\textsf{Hence, sum of parallel sides is \textbf{64 cm}}}.$