Question

In the given figure, find the area of the shaded portion, if four identical square of
side 2 cm are cut from each corner of the rectangle whose length is 25 cm and
breadth is 15 cm.​

Answer 1

Answer :-

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

Here the concept of Areas of Square and Areas of Rectangle has been used. We see that their are four squares at corner of equal dimension. So first we can find area of single square. And then we can find area of rectangle. The area of shaded portion is the area obtained after subtracting the area of 4 square from the area of rectangle.

Let's do it !!

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★ Equations Used :-

$\\\;\boxed{\sf{Area\;of\;Square\;=\;\bf{(Side)^{2}}}}$

$\\\;\boxed{\sf{Area\;of\;Rectangle\;=\;\bf{Length\;\times\;Breadth}}}$

$\\\;\boxed{\sf{Area\;of\;shaded\;portion\;=\;\bf{Area\;of\;Rectangle\;-\;4(Area\;of\;each\;Square)}}}$

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★ Solution :-

Given,

» Side of each square = 2 cm

» Length of each square = 25 cm

» Breadth of each square = 15 cm

» Number of squares at corner = 4

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~ For Area of each Square ::

$\\\;\;\sf{:\rightarrow\;\;Area\;of\;each\;Square\;=\;\bf{(Side)^{2}}}$

$\\\;\;\sf{:\rightarrow\;\;Area\;of\;each\;Square\;=\;\bf{(2)^{2}}}$

$\\\;\;\underline{\underline{\bf{:\rightarrow\;\;Area\;of\;each\;Square\;=\;\bf{4\;\;cm^{2}}}}}$

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~ For Area of the Rectangle ::

$\\\;\;\sf{:\Longrightarrow\;\;Area\;of\;Rectangle\;=\;\bf{Length\;\times\;Breadth}}$

$\\\;\;\sf{:\Longrightarrow\;\;Area\;of\;Rectangle\;=\;\bf{25\;\times\;15}}$

$\\\;\;\underline{\underline{\bf{:\Longrightarrow\;\;Area\;of\;Rectangle\;=\;\bf{375\;\;cm^{2}}}}}$

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~ For Area of Shaded Region ::

$\\\;\;\sf{:\mapsto\;\;Area\;of\;shaded\;portion\;=\;\bf{Area\;of\;Rectangle\;-\;4(Area\;of\;each\;Square)}}$

$\\\;\;\sf{:\mapsto\;\;Area\;of\;shaded\;portion\;=\;\bf{375\;-\;4(4)}}$

$\\\;\;\sf{:\mapsto\;\;Area\;of\;shaded\;portion\;=\;\bf{375\;-\;16}}$

$\\\;\;\underline{\underline{\bf{:\mapsto\;\;Area\;of\;shaded\;portion\;=\;\bf{359\;\;cm^{2}}}}}$

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;Shaded\;\;Region\;=\;\bf{359\;\;cm^{2}}}}}$

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★ More to know :-

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

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

$\\\;\sf{\leadsto\;\;Area\;of\;Trapezium\;=\;\dfrac{1}{2}\;\times\;(Sum\;of\;||^{el}\;sides)\;\times\;Height}$

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

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

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

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

Answer 2

$\large\purple{\mid{\boxed{\sf{Answer⤵}}\mid}}$

➡ Area of shaded region is 359cm²

Given,

Side of each square = 2cm

Length of each square = 25cm

Breadth of each square = 15cm

Number of squares at corner = 4

Area of Square :-

$\large\sf area \: of \: each \: square = ({side}^{2})$

$\large\sf area \: of \: each \: square = ( {2}^{2})$

$\large\pink{\boxed{\sf{Area\: of\: square=4cm}}}$

Area of Rectangle :-

$\large\sf area \: of \: rectangle = length \times breadth$

$\large\sf area \: of \: rectangle = 25 \times 15$

$\large\orange{\boxed{\sf{Area\: of\: rectangle=375cm²}}}$

Area of shaded region :-

$\large\sf area \: of \: shaded \: region = area \: of \: rectangle \: - 4 times \: area \: of \: square$

$\large\sf area \: of \: shaded \: region = 375 - 4(4)$

$\large\sf area \: of \: shaded \: region = 375 - 16$

$\large\red{\boxed{\sf{Area\: of\: shaded\: region=375cm²}}}$

Hope it helps..

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