Answer:
[tex](17 + 7 \sqrt{7} ) {m}^{2} [/tex]
Step-by-step explanation:
Area of a rectangle = Length × Width
Length given = [tex](3 + \sqrt{7} )m[/tex]
Width given =[tex](1 + 2 \sqrt{7} )m[/tex]
Area of the rectangle =
[tex](3 + \sqrt{7} ) \times (1 + 2 \sqrt{7} )[/tex]
[tex] = > 3(1 + 2 \sqrt{7} ) + \sqrt{7} (1 + 2 \sqrt{7} )[/tex]
[tex] = > 3 + 6 \sqrt{7} + \sqrt{7} + 2 \times { (\sqrt{7} )}^{2} [/tex]
[tex] = > 3 + 6 \sqrt{7} + \sqrt{7} + 2 \times 7[/tex]
[tex] = > 14 + 3 + 7 \sqrt{7} [/tex]
[tex] = > (17 + 7 \sqrt{7} ) {m}^{2} [/tex]
