ANSWER
[tex]7 {m}^{2} [/tex]
EXPLANATION
If the area of the circle is 84π m² , then the area of a 30° sector is just a proportion of the full circle.
The area of the 30° sector is
[tex] \frac{30}{360} \times 84\pi \: {m}^{2} [/tex]
[tex] = \frac{1}{12} \times 84 {m}^{2} [/tex]
[tex] = 7 {m}^{2} [/tex]
Hence the area of the 30° sector of this circle is
[tex]7 {m}^{2} [/tex]
