Question

Find the area of the shaded region. Round your answer to the nearest tenth.
please help

Answer 1

38.52 cm²

Explanation:

Take the shaded area to be found into 2 parts :

1. Left sector
2. Top area subtended by the chord

Area of left sector

• As the area subtended by the chord takes up an angle of 120°, the remaining angle of the semicircle is :
• 180° - 120° = 60°
• Area = πr² x (angle of sector)/360°
• Area = 3.14 x (6)² x 60/360
• Area = 3.14 x 36 x 1/6
• Area = 3.14 x 6
• Area = 18.84 cm²

Area subtended by top chord

• Area (120° sector) - Area (triangle)
• Area = πr² x θ/360 - 1/2bh
• Area = 3.14 x 36 x 120/360 - 1/2 x 6 x 6
• Area = 3.14 x 12 - 18
• Area = 37.68 - 18
• Area = 19.68 cm²

Area (shaded)

• Area (left sector) + Area (subtended by chord)
• 18.84 + 19.68
• 38.52 cm²

Answer 2

41.0 cm^2 to nearest tenth.

Explanation:

Required area = Area of the semicircle - area of the clear triangle

Area semicircle = 0.5πr^2

= 0.5π *6^2

= 18π.

Finding Altitude h of the triangle :

cos 60 = h / 6

h = 6 cos 60 = 6 * 1/2

= 3.

Finding Base b of the triangle:

sin 60 = 0.5b / 6

0.5b = 6 * sin 60

= 5.196.

So area of the triangle = h * 0.5b

= 3 * 5.196

Area of shaded region

= 18π - 3 * 5.196

= 40.96 cm^2