Question

If the Perimeter of a Trapezium be 52cm , it's non-parallel sides are equal to 10cm each and its altitude is 8cm , find the area of the Trapezium.​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• If the Perimeter of a Trapezium be 52cm , it's non-parallel sides are equal to 10cm each and its altitude is 8cm , find the area of the Trapezium.

$\large\underline{ \underline{ \sf \maltese{ \: Given:- }}}$

• Perimeter of Trapezium = 52cm
• Altitude of Trapezium = 8cm
• Non- Parallel Side = 10cm each

$\large\underline{ \underline{ \sf \maltese{ \: To \: Find:- }}}$

• Area of Trapezium ?

$\large\underline{ \underline{ \sf \maltese{ \: </strong><strong>Solution</strong><strong>:- }}}$

$\underbrace\red{\boxed{ \sf \blue{Perimeter \: of \: Trapezium }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Sum \: of \: the \: Parallel \: Sides \: + \: Sum \: of \: the \: Non-Parallel \: Sides }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Sum \: of \: the \: Parallel \: Sides \: + \: 2 \: \times \: 10 \: = \: 52 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Sum \: of \: the \: Parallel \: Sides \: + \: 20 \: = \: 52 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Sum \: of \: the \: Parallel \: Sides \: = \: 52\: - \: 20 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Sum \: of \: the \: Parallel \: Sides \: = \: 32cm }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ Sum \: of \: the \: Parallel \: Sides\: = \: 32cm }}}$

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$\underbrace\red{\boxed{ \sf \blue{Area \: of \: Trapezium }}}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: Area \: of \: Trapezium \: = \: \frac{1}{2} \: \times \: ( Sum \: of \: the \: Parallel \: Sides) \: \times \: Altitude }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Area \: of \: Trapezium \: = \: \frac{1}{2} \: \times \: 32 \: \times \: 8}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Area \: of \: Trapezium \: = \: \frac{1}{\cancel 2} \: \times \: 32 \: \times \: \cancel 8}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Area \: of \: Trapezium \: = \: 1 \: \times \: 32 \: \times \: 4}}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ Area \: of \: Trapezium\: = \: 128{cm}^{2} }}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Area \: of \: Trapezium \: = \underline {\underline{128{cm}^{2} }}}\\\end{gathered}\end{gathered}$

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Answer 2

Step-by-step explanation:

$perimeter = 52cm \\ a + b + 10 + 10 = 52 \\ a + b = 32cm \\ h = 8cm \\ \\ area \: = \frac{1}{2} (a + b) \times h \\ \\ area = \frac{1}{2} \times 32 \times 8 \\ \\ = 128 {cm}^{2}$