Question

The area of a trapezium is 400 cm², the distance between the parallel sides is 16 cm. If one of the parallel sides is 20 cm, find the length of the other side.​

Answer 1

$\large\sf\underline{Given:-}$

• $\sf\:Area\:of\:trapezium=400cm^{2}$

• $\sf\:Distance\:between\:parallel\:sides=16cm$

• $\sf\:One\:Parallel\:sides=20cm$

$\large\sf\underline{Solution:-}$

We know,

$\sf\:Area\:of\:trapezium$

$\tt\pink{=\:\frac{1}{2} \times Sum\:of\:parallel\:Sides \times ⊥ distance \:between \:them}$

Let the length of other parallel side be x cm.

Now let's substitute the given values in the formula :

$\sf\:Area\:of\:trapezium=400cm^{2}$

$\tt\pink{⟹\:\frac{1}{2} \times Sum\:of\:parallel\:Sides \times ⊥ distance \:between \:them=400cm^{2}}$

$\sf⟹\:\frac{1}{2} \times (20+x) \times 16 =400cm^{2}$

$\sf⟹\:\frac{20+x}{2} \times 16 =400cm^{2}$

$\sf⟹\:\frac{320+16x}{2} =400$

$\sf⟹\:320+16x =400 \times 2$

$\sf⟹\:320+16x =800$

$\sf⟹\:16x =800 -320$

$\sf⟹\:16x =480$

$\sf⟹\:x =\frac{480}{16}$

$\tt\pink{⟹\:x =30cm}$

So the other parallel side is 30 cm.

Scroll left to right to view your answer properly !

• Thnku ❣

Answer 2

Answer :-

• The length of the other parallel side of trapezium is 30cm.

Step-by-step explanation :

To Find :-

• The length of the other side of trapezium

Solution :-

Given that,

• Area of trapezium = 400 cm²
• Distance between the two parallel sides = 16 cm
• One parallel side of trapezium = 20 cm

As we know that,

Area of trapezium = 1/2 × ( a + b ) × h,

Where,

• a and b are the two parallel sides of trapezium
• h is the distance between two parallel sides.

Assumption: Let us assume the unknown length of trapezium as a.

Therefore,

=> 1/2 × ( a + 20 ) × 16 = 400

Dividing 2 and 16 with 2,

=> 1 × ( a + 20 ) × 8 = 400

=> a + 20 × 8 = 400

Transposing 8 to R.H.S from L.H.S,

=> a + 20 = 400/8

=> a + 20 = 50

Transposing 20 to R.H.S from L.H.S,

=> a = 50 - 20

=> a = 30

• Hence, the length of the other parallel side of trapezium is 30cm.