Question

On a rectangular field, whose length is 25m and width is 10m, a house is built in the shape of a square,whose one side is 9m .Find the area of only the shaded region . *​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that, On a rectangular field, whose length is 25m and width is 10m, a house is built in the shape of a square, whose one side is 9m.

Dimensions of rectangular field

Length of rectangular field = 25 m

Breadth of rectangular field = 10 m

So,

$\rm \: Area_{(rectangular\:field)} = Length \times Breadth$

$\rm \: Area_{(rectangular\:field)} = 25 \times 10$

$\rm\implies \:Area_{(rectangular\:field)} = 250 \: {m}^{2}$

Dimensions of square shape room

Side of room = 9 m

$\rm \: Area_{(square)} = {(side)}^{2}$

$\rm \: Area_{(square)} = {(9)}^{2}$

$\rm\implies \:Area_{(square)} = 81 \: {m}^{2}$

Now,

$\rm \: Area_{(shaded \: region)}$

$\rm \: = \: Area_{(rectangular\:field)} - Area_{(square)}$

$\rm \: = \: 250 - 81$

$\rm \: = \: 169 \: {m}^{2}$

Hence,

$\color{green}\rm\implies \:\boxed{ \rm{ \:\rm \: Area_{(shaded \: region)} \: = \: 169 \: {m}^{2} \: \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

Answer:

169 is the right answer

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