Question

Find the area of the shaded region.
Round to the nearest tenth.

Answer 1

Area shaded blue = 294.5 m^2 (to the nearest tenth)

Explanation:

Refer to the attached figure.

Consider sector patterned in orange

radius = 11.1 m

angle of sector = 360-130 = 230 degrees

area of sector = (angle / 360) * area of complete circle

A1 = (230/360)*pi * 11.1^2

= 78.7175 pi

= 247.298 m^2

Area of right triangle with hypotenuse, L, and one of the angles, x, known

= (Lsin(x))*L(cos(x)/2

= L^2 sin(2x)/4

A2 = 2* (11.1^2 sin(130/2)/4)

= 11.1^2 * sin(65) / 2

= 47.192 m^2

Area shaded blue

= A1+A2

= 247.298 + 47.192

= 294.49 m^2