Question

the area of a parallelogram on a base 56 M long is the same as that of the area of triangle with base 72 hours and height 42 M find the height of the parallelogram​

Answer 1

Given :

• Area of Parallelogram = 56 m
• Area of Parallelogram = Area of Triangle
• Base of Triangle = 72 m
• Height of Triangle = 42 m

To Find :

• Height of Parallelogram = ?

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SolutioN :

$\dag$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Triangle)}} = \dfrac{1}{2} \times Base \times Height }}}}}$

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Parallelogram)}} = Base \times Height }}}}}$

$\dag$ Calculating the Height :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { Area{\small_{(Triangle)}} = Area{\small_{(Parallelogram)}} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{1}{2} \times Base \times Height = Base \times Height } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{1}{2} \times 72 \times 42 = 56 \times Height } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{1}{2} \times 3024 = 56 \times Height } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{3024}{2} = 56 \times Height } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \cancel\dfrac{3024}{2} = 56 \times Height } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 1512 = 56 \times Height } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \dfrac{1512}{56} = Height } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \cancel\dfrac{1512}{56} = Height } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf { Height = 27 \; m }}}}} \; {\pink{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Height of the Parallelogram is 27 m .

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Answer 2

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QUESTIONS:-

the area of a parallelogram on a base 56 M long is the same as that of the area of triangle with base 72 hours and height 42 M find the height of the parallelogram.

ANSWER:-

Calculating the Height:-

Area (triangle) = Area (parallelogram)

=> 1/2 x Base Height x Base x Height

=> 1/2 x 72 x 42 = 56 x Height

=> 1/2 x 3024 = 56 x Height

=> 3024/2 = 56 x Height ( 3024 and 2 are cancelled)

=> 1512 = 56 x Height

=> 1512 / 56 = Height ( 1512 and 56 are cancelled)

=> Height = 27m (ans)

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