Answer:
≈ 11.34 units²
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x + 3.5)² + (y - 2.82)² = 25 ← is in standard form
with r² = 25 ⇒ r = [tex]\sqrt{25}[/tex] = 5
The area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{52}{360}[/tex]
= π × 5² × [tex]\frac{52}{360}[/tex]
= π × 25 × [tex]\frac{52}{360}[/tex]
= [tex]\frac{25(52)\pi }{360}[/tex]
≈ 11.34 units² ( to the nearest hundredth )
