Answer:
(9π - 18) m²
Explanation:
Area of sector = (angle / 360) X area of circle
Length of arc = (angle / 360) X circumference of circle
Area of circle = π r ²
= π (6) ²
= 36π
angle TSR = 90° (the little square means 90). there are 360° in a full circle.
area of sector (the triangle including the shaded part) = (90/360) X 36π
= 9π.
now we need to find the area of the triangle.
ST and SR will be same length (both are radius).
this means that angles STR and SRT will be equal.
there are always 180° in a triangle.
if TSR is 90°, then STR and SRT combined will be 180 - 90 = 90°.
since they are both equal, STR = 45° and SRT = 45°.
Area of triangle = ½ ab sin C (where a and b are the side lengths, ie both are 6, C is the angle between them. ie 90°)
= 1/2 (6) (6) Sin 90
= 18.
we now have the area of our sector (9π) and area of our triangle (18).
the shaded section is the difference between the two.
so we just subtract the area of the triangge from the area of the sector:
9π - 18 = (9π - 18) m² ........ this roughly = 10.27 m²