Question

Q2. If the area of a Trapezium is 48cm². Find one of its parallel sides if another parallel side is of 12cm and distance between the parallel sides is 6 cm.​

Answer 1

$\purple {\underline{ \huge{\purple{ \mathfrak{Given:}}}}}$

• Area of trapezium = 48 cm²
• One parallel side = 12 cm
• Height of trapezium = distance between parallel sides = 6 cm

$\purple {\underline{ \huge{\purple{ \mathfrak{To \: Find:}}}}}$

• Another parallel side of trapezium

$\purple {\underline{ \huge{\purple{ \mathfrak{Solution:}}}}}$

• Let another parallel side be x

$\: \: \: \: \: \: \: \: \: \: \: \: \: \rm{ \underline{Formula \: to \: find \: area \: of \: trapezium}}$

$\boxed{ \red{ \large{ \mathfrak{area = \frac{sum \: of \: parallel \: sides}{2} \times height}}}}$

According to question,

$\large{ \sf : \implies \: \: \: \: \: \: \: \: \frac{x + 12}{2} \times 6 = 48}$

$\large{ \sf : \implies \: \: \: \: \: \: \: \: \frac{x + 12}{2} = \frac{48}{6} }$

$\large{ \sf : \implies \: \: \: \: \: \: \: \:x + 12 = 8 \times 2}$

$\large{ \sf : \implies \: \: \: \: \: \: \: \:x + 12 = 16}$

$\large{ \sf : \implies \: \: \: \: \: \: \: \:x = 16 - 12}$

$\large{ \sf : \implies \: \: \: \: \: \: \: \:x = 4}$

$\purple {\underline{ \huge{\purple{ \mathfrak{Hence:}}}}}$

• The Length of another parallel side is 4 cm

Answer 2

$\large\bf{\underline\red{Good \: Afternoon♡}}$

Question :-

If the area of a Trapezium is 48cm². Find one of its parallel sides if another parallel side is of 12cm and distance between the parallel sides is 6 cm.

Answer :-

Given:-

One of the parallel sides = 12cm

Let the length of the other parallel sides be 'x' cm

Also, area of the trapezium = 48 cm²

Distance between the parallel sides = 6cm

Area of trapezium = $\frac{1}{2} \times (a + b) \times h$

$48 = \frac{1}{2} \times (12 + x) \times 6$

$48 \times 2 = (12 + x) \times 6$

$96 = 72 + 6x$

$6x = 96 - 72$

$6x = 24$

$x = \frac{24}{6}$

$x = 4$

Hence, the length of the other parallel sides is 4cm