Question

If the area of a trapezium is 265 sq. cm and the perpendicular distance between its parallel sides is 10 cm, then find the sum of its parallel sides.​

Answer 1

Given :

• Area of the Trapezium = 265 cm²
• Distance between parallel Sides = 10 cm

To Find :

• Sum of Parallel Sides = ?

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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 = First Parallel Side
• b = Second Parallel Side

$\dag$ Calculating the Sum :

$\begin{gathered} \; \; \qquad \longmapsto \; \; \sf { Area = \dfrac{ 1}{2} \times \bigg( a + b \bigg) \times Height } \\ \\ \\ \\ \ \; \; \longmapsto \; \; \sf { 265 = \dfrac{1}{2} \times \bigg( a + b \bigg) \times 10 } \\ \\ \\ \ \; \; \longmapsto \; \; \sf { 265 \times 2 = 1 \times \bigg( a + b \bigg) \times 10 } \\ \\ \\ \\ \ \; \; \longmapsto \; \; \sf { 530 = 1 \times \bigg( a + b \bigg) \times 10 } \\ \\ \\ \ \; \; \longmapsto \; \; \sf { \dfrac{530}{10} = 1 \times \bigg( a + b \bigg) } \\ \\ \\ \\ \ \; \; \longmapsto \; \; \sf { \cancel\dfrac{530}{10} = 1 \times \bigg( a + b \bigg) } \\ \\ \\ \\ \ \; \; \longmapsto \; \; {\pmb{\underline{\boxed{\purple{\pmb{\frak{ a + b = 53 \; cm }}}}}}} \end{gathered}$

$\therefore \;$ Sum of two Parallel Sides is 53 cm .

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