Question

In the adjoining figure, find:
(i) Perimeter of the given figure
(ii) Area of the given figure.​

Answer 1

Answer:

31cm is perimeter if given figure

Step-by-step explanation:

To find perimeter of any shape u need to add all the sides

7+7+6+3+3+3+2=31

Answer 2

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

Here the Concept of Perimeter and Area of Rectangle has been used. This is done by sum of all sides. This will be give us the perimeter. Now for area, we need to calculate the area of bigger rectangle and subtract the area which is reduced. By this we can find the answer.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{Perimeter\;of\;the\;Figure\;=\;\bf{Sum\;of\;all\;Sides}}}$

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

$\\\;\boxed{\sf{Area\;of\;given\;Figure\;=\;\bf{Area\;of\;bigger\;Rectangle\;-\;Area\;of\;Smaller\;Rectangle}}}$

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★ Solution :-

Given,

» Bigger Figure = Rectangle

» Dimensions of bigger Rectangle = 7 cm × 6 cm

Since its rectangle, then opposite sides will be equal. This means the side of 6 cm is equal to the side from which a part has been reduced. So the length of the part will be -

✒ 6 - (3 + 2) = 1 cm

From this we get,

» Dimension of smaller Rectangle = 3 cm × 1 cm

» All different sides = 7 cm, 6 cm, 7 cm, 3 cm, 3 cm, 1 cm, 3 cm and 2 cm

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i.) ~ For the Perimeter of the Figure ::

This is given as,

$\\\;\;\sf{:\rightarrow\;\;Perimeter\;of\;the\;Figure\;=\;\bf{Sum\;of\;all\;Sides}}$

$\\\;\;\sf{:\rightarrow\;\;Perimeter\;of\;the\;Figure\;=\;\bf{7\;+\;6\;+\;7\;+\;3\;+\;3\;+\;2\;+\;1\;+\;3}}$

$\\\;\;\sf{:\rightarrow\;\;Perimeter\;of\;the\;Figure\;=\;\bf{7\;+\;6\;+\;7\;+\;3\;+\;3\;+\;2\;+\;1\;+\;3}}$

$\\\;\;\bf{:\rightarrow\;\;Perimeter\;of\;the\;Figure\;=\;\bf{32\;\;cm}}$

$\\\;\underline{\boxed{\tt{Perimeter\;\;of\;\;the\;\;figure\;=\;\bf{32\;\;cm}}}}$

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ii.) For the Area of the Figure ::

Firstly, let's calculate the area of bigger rectangle. This is given as,

$\\\;\;\sf{:\Longrightarrow\;\;Area\;of\;Rectangle_{(Bigger)}\;=\;\bf{Length\;\times\;Breadth}}$

$\\\;\;\sf{:\Longrightarrow\;\;Area\;of\;Rectangle_{(Bigger)}\;=\;\bf{6\;\times\;7}}$

$\\\;\;\underline{\underline{\bf{:\Longrightarrow\;\;Area\;of\;Rectangle_{(Bigger)}\;=\;\bf{42\;\;cm^{2}}}}}$

Now let's calculate the area of smaller triangle. This is given as,

$\\\;\;\sf{:\Longrightarrow\;\;Area\;of\;Rectangle_{(Smaller)}\;=\;\bf{Length\;\times\;Breadth}}$

$\\\;\;\sf{:\Longrightarrow\;\;Area\;of\;Rectangle_{(Smaller)}\;=\;\bf{3\;\times\;1}}$

$\\\;\;\underline{\underline{\bf{:\Longrightarrow\;\;Area\;of\;Rectangle_{(Smaller)}\;=\;\bf{3\;\;cm^{2}}}}}$

Then, area of the figure is given as,

$\\\;\;\sf{:\mapsto\;\;Area\;of\;given\;Figure\;=\;\bf{Area\;of\;bigger\;Rectangle\;-\;Area\;of\;Smaller\;Rectangle}}$

$\\\;\;\sf{:\mapsto\;\;Area\;of\;given\;Figure\;=\;\bf{42\;-\;3}}$

$\\\;\;\bf{:\mapsto\;\;Area\;of\;given\;Figure\;=\;\bf{42\;\;cm^{2}}}$

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;the\;\;figure\;=\;\bf{39\;\;cm^{2}}}}}$

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★ More Formulas to Know :-

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

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

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

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

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

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

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