Question

Find the distance between the parallel sides of a trapezium whose area is 288 cm² and parallel sides are respectively 10cm,8 cm​

Answer 1

Question:-

Find the distance between the parallel sides of a trapezium whose area is 288 cm² and parallel sides are respectively 10cm,8 cm

Answer:-

• The height of trapezium is 32 cm.

To find:-

• Height of trapezium

Solution:-

• Area of trapezium = 288 cm²
• Parallel sides = 10 cm and 8 cm

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,

$\large{ \tt : \implies \: \: \: \: \: \: \: \frac{10 + 8}{2} \times h = 288}$

$\large{ \tt : \implies \: \: \: \: \: \: \: \frac{18}{2} \times h = 288}$

$\large{ \tt : \implies \: \: \: \: \: \: \: 9 \times h = 288}$

$\large{ \tt : \implies \: \: \: \: \: \: \: h = \frac{288}{9} }$

$\large{ \tt : \implies \: \: \: \: \: \: \: h = 32}$

Hence,

• The height of trapezium is 32 cm.

Answer 2

Given:

• Area of trapezium :- 288 cm²
• Parallel sides are :- 10 cm, 8 cm

⠀⠀

To Find:

• Height of trapezium.

⠀⠀

Solution:

$\begin{gathered}\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\\end{gathered}$

$\begin{gathered}\star\;{\boxed{\sf{\pink{ Area : \frac{a+b}{2} × h }}}}\\ \\\end{gathered}$

$\begin{gathered}\dag\;{\underline{\frak{Putting\; the\; values\;in\;the\;formula,}}}\\ \\\end{gathered}$

$\; \; \; \; \; \; \; \; \; \; \;\begin{gathered}:\implies\sf \frac{10+8}{2} \times h = 288\\ \\\end{gathered}$

$\; \; \; \; \; \; \; \; \; \; \;\begin{gathered}:\implies\sf \frac{18}{2} \times h = 288\\ \\\end{gathered}$

$\; \; \; \; \; \; \; \; \; \; \;\begin{gathered}:\implies\sf 9 \times h = 288\\ \\\end{gathered}$

$\; \; \; \; \; \; \; \; \; \; \;\begin{gathered}:\implies\sf { h = \dfrac{288}{9}}\\ \\\end{gathered}$

$\; \; \; \; \; \; \; \; \; \; \;\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{h = 32}}}}}\;\bigstar\\ \\\end{gathered}$

Hence,

• Height of trapezium = 32 cm².