Question

The shape of the top surface of a table is a trapezium. Find its area if its parallel sides
are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.

Answer 1

Answer :-

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept\;:-}}}$

Here the Concept of Area of Parallelogram has been used. We see we are already given the dimensions of Trapezium. We can apply its value and find the answer.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;(Sum\;of\;Parallel\;Sides)\;\times\;Height}}}$

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★ Solution :-

Given,

» First Parallel Side = 1 m

» Second Parallel Side = 1.2 m

» Perpendicular Distance between them = Height = 0.8 m

Now area of Trapezium is given as,

$\\\;\;\;\sf{:\mapsto\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;(Sum\;of\;Parallel\;Sides)\;\times\;Height}}$

$\\\;\;\;\sf{:\mapsto\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;(1\;+\;1.2)\;\times\;0.8}}$

$\\\;\;\;\sf{:\mapsto\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;2.2\;\times\;0.8}}$

$\\\;\;\;\sf{:\mapsto\;\;Area\;of\;Trapezium\;=\;\bf{1.1\;\times\;0.8}}$

$\\\;\;\;\sf{:\mapsto\;\;Area\;of\;Trapezium\;=\;\bf{0.88\;\;m^{2}}}$

$\\\;\large{\underline{\underline{\rm{Thus,\;area\;of\;Table\;top\;is\;\;\boxed{\bf{0.88\;\;m^{2}}}}}}}$

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★ More Formulas To Know :-

$\\\;\tt{\leadsto\;\;Area\;\;of\;\;Square\;=\;(Side)^{2}}$

$\\\;\tt{\leadsto\;\;Area\;\;of\;\;Rectangle\;=\;Length\;\times\;Breadth}$

$\\\;\tt{\leadsto\;\;Area\;\;of\;\;Circle\;=\;\pi r^{2}}$

$\\\;\tt{\leadsto\;\;Area\;\;of\;\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

$\\\;\tt{\leadsto\;\;Area\;\;of\;\;Parallelogram\;=\;Base\;\times\;Height}$

$\\\;\tt{\leadsto\;\;Perimeter\;\;of\;\;Square\;=\;4\;\times\;(Side)}$

$\\\;\tt{\leadsto\;\;Perimeter\;\;of\;\;Rectangle\;=\;2\;\times\;(Length\;+\;Breadth)}$

$\\\;\tt{\leadsto\;\;Perimeter\;\;of\;\;Circle\;=\;2\pi r}$

Answer 2

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$\underline{\green {\sf Given:- }}$

• First parallel side = 1 m

• Second parallel side = 1.2 m

• Perpendicular distance between them = 0.8 m

$\underline{\pink {\sf To\:Find:- }}$

• Area of the trapezium = ?

$\underline{\orange {\sf Solution:- }}$

We know that,

$\large\boxed{\underline{\purple{\sf  Area\:of\:the\:trapezium = \dfrac{1}{2} \times (a+b)\times h  }}}$

Here,

→ a = 1.2 m

→ b = 1 m

$⇢ \:\: \sf{\dfrac{1}{2} \times (1.2 + 1) \times 0.8}$

$⇢ \:\: \sf{\dfrac{1}{2} \times 2.2 \times 0.8}$

$⇢\:\: \underline{\boxed{\pink{\mathfrak{0.88\:m^2}}}}$

$\displaystyle\therefore\:\underline{\textsf{The required area is\textbf{ 0.88 m² }}}$

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