Question

the sum of the lengths of the parallel sides of a trapezium is 24cm and its area is 192m^2 find the distance btw the parallel sides​

Answer 1

Question:-

the sum of the lengths of the parallel sides of a trapezium is 24m and its area is 192m² find the distance btw the parallel sides

Answer:-

• The height of trapezium is 16 m

To find:-

• Height of trapezium

Solution:-

• Sum of parallel sides = 24
• Area of trapezium = 192 m²

As we know,

$\large{ \boxed{ \mathfrak{area = \frac{a + b}{2} \times h}}}$

Where,

• a and b = parallel sides
• h = height of trapezium

According to question,

$\large{ \tt : \implies \: \: \: \: \: \: \frac{24}{2} \times h = 192}$

$\large{ \tt : \implies \: \: \: \: \: \: \: h = \frac{192 \times 2}{24} }$

$\large{ \tt : \implies \: \: \: \: \: \: h = 16}$

Hence,

The height of trapezium is 16 m

Answer 2

Correct Question

• The sum of the lengths of the parallel sides of a trapezium is 24m and its area is 192m². Find the distance between the parallel sides.

⠀

Given

• The sum of the length of the parallel side of a Trapezium is 24 m.
• Area of the Trapezium is 192 m².

⠀

To find

• Distance between the parallel sides i.e., height of the trapezium.

⠀

Solution

• Let the parallel sides of the Trapezium be a and b.

⠀

$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Formula\: used}}}$

$\star{\boxed{\sf{\orange{Area_{(Trapezium)} = \dfrac{a + b}{2} \times height}}}}$

⠀

Here,

$\: \: \: \: \: \: \: \: \bullet\bf\: \: \: {a + b = 24}$

$\: \: \: \: \: \: \: \: \bullet\bf\: \: \: {Area = 192}$

⠀

$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Putting\: the\: values}}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {192 = \dfrac{24}{2} \times height}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {192 = 12 \times height}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {height = \dfrac{192}{12}}$

⠀

$\bf:\implies\: \: \: \: \: \: \: \: {height = 16}$

⠀

Hence,

• Height of the Trapezium is 16m.

━━━━━━━━━━━━━━━━━━━━━━