[tex] \large{ \tt{❋ \: EXPLANATION}} : [/tex]
- The formula to find out the volume of a rectangular prism is V = l × b × h where V is the volume , l = length , b = breadth & h = height.
- We're provided the figure of trapezium in the second attachment. The formula to fInd out the area of trapezium is A = [tex] \tt{ \frac{1}{2} h(a + b)}[/tex] where a and b are the opposite parallel sides and h be the height of a trapezium.
[tex] \large{ \tt{❃ \: SOLUTION}} : [/tex]
- In the first picture , we're provided - Length ( l ) = [tex] \frac{7}{4} [/tex] cm , breadth ( b ) = [tex] \frac{3}{2} [/tex] cm and height ( h ) = [tex] \frac{1}{2} [/tex] cm. Now, plug these known values and them find out the volume of given rectangular prism.
[tex] \large{ \tt{❁ \: VOLUME \: OF \: RECTANGULAR \: PRISM \: ( \: V \: ) = l \times b \times h}}[/tex]
[tex] \large{ {⟶ \: \frac{7}{4} \times \frac{3}{2} \times \frac{1}{2} }}[/tex]
- To multiply one fraction by another , multiply the numerators for the numerator and multiply the denominator for its denominator and reduce the fraction obtained after multiplication into lowest term if possible.
[tex] \large{ ⟶ \frac{7 \times 3 \times 1}{4 \times 2 \times 2} }[/tex]
[tex] \large{⟶ \frac{21}{16} \tt{ {cm}^{3} }}[/tex]
- Hence , the volume is [tex] \boxed{ \frac{21}{16} }[/tex] cubic centimetres.
--------------------------------
- In the second attachment , we're provided - 6ft and 7 ft are the opposite parallel sides and 3 ft is the height of the given trapezium.
[tex] \large{ \tt{✺ \: AREA \: OF \: A \: TRAPEZIUM = \frac{1}{2} h(a + b)}}[/tex]
[tex] \large{ ⟶ \frac{1}{2} \times 3(6 + 7)}[/tex]
[tex] \large{⟶ \: \frac{1}{2} \times 3 \times 13 }[/tex]
[tex] \large{⟶ \frac{39}{2} \tt{cm}^{2} }[/tex]
- Hence , The area of trapezium is [tex] \boxed{ \frac{39}{2} \tt{cm}^{2} }[/tex]
And we're done ! ♪
[tex] \large{ \# \: \mathfrak{StayInAndExplore \:☂ }}[/tex]
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
