Question

If the area of a trapezium is 28 cm square and one of its parellel side is 6cm , find the other parellel side if it's altitude is 4cm.​

Answer 1

In the question, it is given that :

• Area of trapezium = 28cm²
• One of the parallel side = 6cm
• Altitude = 4cm

We shall find :

• Other parallel side
• Let the unknown other parallel side be xcm.

We know that :

• Area of trapezium = ½ (Sum of parallel sides) (Altitude)

Now, substituting the values in the formula and solving for x :

• 28cm² = ½ (x + 6cm) (4cm)
• 28 = ½ (4x + 24)
• 28 × 2 = 4x + 24
• 56 = 4x + 24
• 56 - 24 = 4x
• 32 = 4x
• 32/4 = x
• x = 8cm

Therefore, the length of the other parallel side in the trapezium is 8cm.

Answer 2

$\frak{Given} = \begin{cases} &\sf{The\:Area\:of\:the\:Trapezium\:=\:28cm.} \\\\\\ &\sf{One\:parellel\:side\:=\:6cm\:.} \\\\\\ &\sf{Altitude\:=\:4cm}\end{cases}$

$\maltese$ To find:-    

$\qquad\sf{:\implies\:The\:other\:parellel\:side\:.}$

$\maltese$ Assumption Needed:-      

$\qquad\sf{:\implies\:Let\:The\:other\:parellel\:side\:be\:=\:x.}$

$\maltese$ Solution:-      

$\maltese$ Here we have the area of the trapezium, one parallel side of the trapezium and the altitude of the trapezium. so to find the other parallel side we will assume that the other parallel side of the trapezium be x and after this step, we will use the formula.

$\qquad\sf{:\implies\:Area\:_{(Trapezium)}\:=\:\dfrac{1}{2}\:\times\:Sum\:of\:parellel\:side\:\times\:Altitude}$

$\qquad\sf{:\implies\:28\:=\:\dfrac{1}{2}\:(\:X\:+6\:)\:(4)}$

$\qquad\sf{:\implies\:28\:=\:\dfrac{1}{2}\:(\:4x\:+24\:)}$

$\qquad\sf{:\implies\:28\:\times\:2\:=\:4x\:+\:24}$

$\qquad\sf{:\implies\:56 \:=\: 4x\: +\: 24}$

$\qquad\sf{:\implies\:56 \:-\: 24\: =\: 4x}$

$\qquad\sf{:\implies\:32 \:= \:4x}$

$\qquad\sf{:\implies\:x\:=\:\dfrac{32}{4}}$

$\qquad\sf{:\implies\:x\:=\:8cm}$

$\color{orange}{\underline{\sf{Therefore\:the\:othe\:parellel\:side\:of\:the\:trapezium\:is\:8cm\:.}}}$