Answer:
[tex]\boxed{\textsf{ The total surface area of the cuboid is \textbf{62 cm} $\sf ^2$ .}}[/tex]
Step-by-step explanation:
Given that the base area of the cuboid is 7cm² . And it's volume is 21cm³ . We need to find its total surface area . Now here we need to find the height . We can find height as ,
Height :-
[tex]\qquad\boxed{\boxed{\sf Height =\dfrac{ Volume}{Area } }}[/tex]
[tex]\sf\implies Height =\dfrac{Volume}{Area} \\\\\sf\implies h =\dfrac{ 21cm^3}{7cm^2}\\\\\implies \boxed{ \pink{\frak { Height = 3 cm.}}}[/tex]
[tex]\rule{200}2[/tex]
Let's find out the Total surface area .
TSA of cuboid :-
[tex]\qquad\boxed{\boxed{\sf TSA_{(cuboid)} =2(lb + bh + hl ) }}[/tex]
Put on the respective values :-
[tex]\sf\implies TSA_{(cuboid)}= 2( lb + bh + hl )\\\\\sf\implies TSA_{(cuboid)}= 2( 7cm\times 1cm + 1cm\times 3cm + 3cm \times 7 cm ) \\\\\sf\implies TSA_{(cuboid)}=2 ( 7cm ^2+3cm^2+21cm^2 ) \\\\\sf\implies TSA_{(cuboid)}= 2\times 31cm^2 \\\\\sf\implies \boxed{\pink{\frak{ TSA_{(cuboid)}= 62 cm^2}}}[/tex]
