Answer

1. The area of the sector RST is 314 cm².

2. The area of the shaded segment is 114 cm².

Solution

1. For the area of the sector RST,

Given

θ = 90º

radius (r) = 20 cm

Substitution

Area of a Sector of Circle = (θ/360º) × π × r²

Area of a Sector of Circle = (90º/360º) × 3.14 × (20)²

Area of a Sector of Circle = (0.25) × 3.14 × 400

Area of a Sector of Circle = 314 cm²

2. For the area of the shaded segment,

Given

base (also the radius) = 20 cm

height (also the radius) = 20 cm

Substitution

Area of a triangle = 1/2 × base × height

Area of a triangle = 1/2 × 20 cm × 20 cm

Area of a triangle = 1/2 × 400 cm²

Area of a triangle = 200 cm²

Area of the shaded segment = Area of a Sector of Circle - Area of a triangle

Area of the shaded segment = 314 cm² - 200 cm²

Area of the shaded segment = 114 cm²