Question

The Area of trapezium of height 24.2 cm is 605 cm².one of the parrallel sides is 21 cm,find the other side.

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Answer 1

Given :

• Area of Trapezium = 605 cm
• Height of Trapezium = 24.2. cm
• 1st Parallel Side = 21 cm

To Find :

• Find the 2nd Parallel Side

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SolutioN :

$\dag$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Trapezium)}} = \dfrac{1}{2} \times \bigg( a + b \bigg) \times Height }}}}}$

Where :

• a = 1st Parallel Side
• b = 2nd Parallel Side

$\dag$ Calculating the 2nd Parallel Side :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { Area = \dfrac{1}{2} \times \bigg( a + b \bigg) \times Height } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 605 = \dfrac{1}{2} \times \bigg( 21 + b \bigg) \times 24.2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 605 \times 2 = 1 \times \bigg( 21 + b \bigg) \times 24.2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 1210 = 1 \times \bigg( 21 + b \bigg) \times 24.2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 1210 =21 + b \times 24.2 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { \dfrac{1210}{24.2} =21 + b } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { \dfrac{12100}{242} =21 + b } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { \cancel\dfrac{12100}{242} = 21 + b } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 50 = 21 + b } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { 50 - 21 = b } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\frak { 2nd \; Parallel \; Side = 29 \; cm }}}}} {\red{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Second Parallel Side of the Trapezium is 29 cm .

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