Question

I need help from anyone!

Answer 1

h = 10.0708 cm

Area of shaded region = 8.1841
`cm^(2)`

Explanation:

r = radius of circle

= 14 cm

h = perpendicular height of triangle

Use SinФ trigonometric function to determine h

SinФ =
`(Opposite)/(Hypotenuse)`

Sin46° =
`(h)/(14)`

Cross-multiplication is applied:

∴h = (14)(Sin46°)

h = 10.0708 cm (Rounded to four decimal places)

Area of sector =
`(AngleOfSector)/(360^(o))` × (
`\pi r^(2)`)

=
`(46)/(360)` ×
`\pi (14^(2))`

=
`(9016)/(360) \pi`
`cm^(2)`
= 78.68
`cm^(2)`

Area of triangle =
`(1)/(2)` × (Base of triangle) × h

=
`(1)/(2)` × (14 cm) × [(14)(sin46°)]
= (98)(sin46°)

= 70.50
`cm^(2)`

∴Area of yellow shaded region = Area of sector - Area of triangle

= {[
`(9016)/(360) \pi`] - [(98)(sin46°)]}
`cm^(2)`

= 8.1841
`cm^(2)` (Rounded to four decimal places)