Find the Height of the Parallelogram if the Area of Parallelogram is 36 cm² and Base is 9 cm​ and Base in 9 cm ?

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Find the Height of the Parallelogram if the Area of Parallelogram is 36 cm² and Base is 9 cm​ and Base in 9 cm ?

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  1. Given : The Area of Parallelogram is 36 cm² and Base is 9 cm.

    To Find : Height of the Parallelogram ?

    _____________________

    ❍ Let’s consider the Height of the Parallelogram be h.

    [tex]\underline{\frak{As ~we~ know~ that~:}}[/tex]

    • [tex]\boxed{\sf\pink{Area_{(Parallelogram)}~=~b~×~h}}[/tex]★

    [tex]~[/tex]

    Solution : Here b is the Base of Parallelogram in cm & h is the Height of Parallelogram in cm. And we have given with the Area of Parallelogram is 36 cm².

    [tex]~[/tex]

    [tex]\underline{\bf{Now ~By ~Substituting~ the ~Given~ Values~:}}[/tex]

    [tex]~[/tex]

    [tex]~~~~~~~~~~{\sf:\implies{36~cm^{2}~=~9~×~h}}[/tex]

    [tex]~~~~~~~~~~{\sf:\implies{h~=~\dfrac{36}{9}}}[/tex]

    [tex]~~~~~~~~~~{\sf:\implies{h~=~\cancel\dfrac{36}{6}}}[/tex]

    [tex]~~~~~~~~~~:\implies{\underline{\boxed{\frak{\pink{h~4~cm}}}}}[/tex]★

    [tex]~[/tex]

    Hence,

    [tex]\therefore\underline{\sf{Height~ of ~the ~Parallelogram ~is~\bold{4~cm}}}[/tex]

    [tex]~[/tex]

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    V E R I F I C A T I O N :

    [tex]~[/tex]

    [tex]\underline{\frak{As ~we ~know~ that~:}}[/tex]

    • [tex]\boxed{\sf\pink{Area_{(Parallelogram)}~=~b~×~h}}[/tex]★

    [tex]~[/tex]

    Here b is the Base of Parallelogram in cm & h is the Height of Parallelogram in cm. And we have given with the Area of Parallelogram is 36 cm².

    [tex]~[/tex]

    [tex]\underline{\bf{Now~ By ~Substituting ~the ~Given ~and~ Found~ Values~:}}[/tex]

    [tex]~[/tex]

    [tex]~~~~~~~~~~{\rm:\implies{36~cm^{2}~=~9~×~4}}[/tex]

    [tex]~~~~~~~~~~:\implies\boxed{\rm\pink{36~cm^{2}~=~36~cm^{2}}}[/tex]★

    [tex]~~~~[/tex][tex]\qquad\quad\therefore\underline{\textsf{\textbf{Hence Verified!}}}[/tex]

    [tex]~[/tex]

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    More Information :

    [tex]~~~[/tex][tex]\qquad\quad\underline{\textsf{\textbf\pink{Formula’s~of~Areas~:}}}[/tex]

    • [tex]{\rm\leadsto{Square~=~(Side)^2}}[/tex]
    • [tex]{\rm\leadsto{Rectangle~=~Length~×~Breadth}}[/tex]
    • [tex]{\rm\leadsto{Triangle~=~\dfrac{1}{2}~×~Breadth ~×~Height}}[/tex]
    • [tex]{\rm\leadsto{Scalene\triangle~=~\sqrt{s(s~-~a)(s~-~b)(s~-~c)}}}[/tex]
    • [tex]{\rm\leadsto{Rhombus~=~\dfrac{1}{2}~×~d_{1}~×~d_{2}}}[/tex]
    • [tex]{\rm\leadsto{Rhombus~=~\dfrac{1}{2}p\sqrt{4a^{2}~-~p^{2}}}}[/tex]
    • [tex]{\rm\leadsto{Parallelogram~=~ Breadth~×~ Height}}[/tex]
    • [tex]{\rm\leadsto{Trapezium~=~\dfrac{1}{2}(a~+~b)~×~Height}}[/tex]
    • [tex]{\rm\leadsto{Equilateral~Triangle~=~\dfrac{\sqrt{3}}{4}(Side)^2}}[/tex]
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  2. Answer:

    Also, the area of the parallelogram ABCD is equal to 36 cm2. So, AB×x=36. Hence, the height of the parallelogram ABEF is 8.57 cm.

    Best of luck your future

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