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

Correct 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 -:

• $\boxed{\sf{\purple{Area\:of\:\:Shaded \:portion-: 359cm² }}}$

Explanation-:

Given ,

• The length of Rectangle is 25 cm .
• The breadth of Rectangle is 15 cm .
• The length side of a four squares which is at each corner is 2 cm .

To Find ,

• Area of the shaded portion.

Analysis-:

• From the given figure we can see that there is a Rectangle and in the Rectangle we have square at four corners of the rectangle which is not in the part of the shaded region .
• First we have to find the Area of Rectangle and Area of four square which is at four corners.

☆ Figure according to the question-:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 25 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 15 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Then ,

• We have to Subtract the area of four square from the area of Rectangle .

Solution-:

• $\boxed{\sf{\blue {Area \: of \: Rectangle-: \: Length \times Breadth }}}$

Here ,

• The length of Rectangle is 25 cm .
• The breadth of Rectangle is 15 cm.

Now ,

$\pink{\sf{\rightarrow {Area\:of\:Rectangle\:-: 25 cm \times 15cm }}}$

$\pink{\sf{\rightarrow {Area\:of\:Rectangle\:-: 375 cm² }}}$

Therefore,

• $\boxed{\sf{\purple{Area\:of\:Rectangle\:-: 375 cm² }}}$ .................(1)

Now ,

• $\boxed{\sf{\blue {Area \: of \: Square: \: = Side \times Side}}}$

Here ,

• The side of a square is 2 cm .

Now ,

$\pink{\sf{\rightarrow {Area\:of\:Square \:-: 2cm \times 2cm }}}$

$\pink{\sf{\rightarrow {Area\:of\:Square \:-: 4cm² }}}$

Therefore,

• $\boxed{\sf{\purple{Area\:of\:Square\:-: 4 cm² }}}$ .....................(2)

Now ,

• $\boxed{\sf{\blue {Area \: of \:four\: Square: \: = 4 \times Area \: of\: square}}}$

Here ,

• Area of square-: 4 cm² . .........[From 2]

Now ,

$\pink{\sf{\rightarrow {Area\:of\:four\:Square \:-: 4 \times 4cm²}}}$

$\pink{\sf{\rightarrow {Area\:of\:four\:Square \:-: 16cm²}}}$

Hence ,

$\boxed{\sf{\purple{Area\:of\:four\:Square\:-: 16 cm² }}}$ ...........(3)

Now ,

☆ Area of shaded portion-: Area of Rectangle - Area of four square which is at corners

• Area of Rectangle -: 375 cm² . ................[From 1]
• Area of four square which is at four corners-: 16 cm² . ..............[From 3]

Now ,

$\pink{\sf{\rightarrow {Area\:of\:four\:Shaded \:portion\:-: 375 cm² - 16 cm²}}}$

$\pink{\sf{\rightarrow {Area\:of\:four\:Shaded \:portion\:-: 359cm²}}}$

Hence ,

• $\boxed{\sf{\purple{Area\:of\:\:Shaded \:portion-: 359cm² }}}$

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