There is a semicircular O with radius 6 cm as shown in the figure below.
The circumference of the semicircular is divided into 6 equal parts.
The circumference of the semicircular is divided into 6 equal parts.
(6)-1 Find the area of triangle OAB.
(6)-2 Find the area of the shaded portion.
Answer
(6)-1 6 cm2
(6)-2 33.84 cm2
Solution
(6)-1 Since ∠AOB = 30 degrees as shown in the figure below, the height of △OAB = 6 cm × 1/2 = 3 cm.
Therefore the area of △AOB = 4 × 3 × 1/2 = 6 cm2.
(6)-2 The area of shaded portion = △OCD + Sector OAC + △OAB = 3 × 6 × 1/2 + 6 × 6 × 3.14 × 60/360 + 6 = 9 + 18.84 + 6 = 33.84 cm2.
