Answer:
294.5 m²
Step-by-step explanation:
shaded region = area of major sector + area of triangle
central angle of major sector = 360° - 130° = 230°
area of sector = area of circle × fraction of circle
A = π × 11.1² × [tex]\frac{230}{360}[/tex]
= [tex]\frac{x11.1^2(230)\pi }{360}[/tex] ≈ 247.3 m²
area of triangle = 0.5 × 11.1 × 11.1 × sin130° ≈ 47.2 m²
shaded area = 247.3 + 47.2 ≈ 294.5 m²
Answer:
294.5 m^2 to the nearest tenth.
Step-by-step explanation:
First work out the area of the blue sector (not including the triangle):
The measure of the large arc = 360 - 130 = 230 degrees and the area of the Whole circle is π(11.1)^2 so, by proportion:
Area of the large sector = 230/360 * π(11.1)^2
= 247.30 m^2.
The area of the triangle = 1/2 * 11.1^2 sin 130 = 47.19 m^2.
So the area of the whole shaded region is 247.30 + 47.19
= 294.49 m^2 (answer)
