Question

what percentage of triangle LMN is shaded​

Answer 1

Answer:

37.5%

Step-by-step explanation:

Answer 2

Answer:

Side of Equilateral Triangle, a = 14 cm

Angle of sector,

\theta = 60 \degreeθ=60°

radius of sector, r = 7 cm

Ans: (1)

Area of an equilateral triangle =

\begin{gathered} \frac{ \sqrt{3} }{4} {a}^{2} \\ = > \frac{ \sqrt{3} }{4} \times {14}^{2} = 49 \sqrt{3} {cm}^{2} \end{gathered}43a2=>43×142=493cm2

Ans: (2)

Area of a sector

\begin{gathered} = \frac{\pi {r}^{2} }{360 \degree} \times \theta = \frac{\pi \times {7}^{2} }{360 \degree} \times 60 \degree \\ = > \frac{49\pi}{6} {cm}^{2} \end{gathered}=360°πr2×θ=360°π×72×60°=>649πcm2

Ans:(3) Since, All sectors are of same measure :

Total Area of Three sectors :

3*Area of one sector

=>

3 \times \frac{49\pi}{6} = \frac{49\pi}{2} {cm}^{2}3×649π=249πcm2

4) Area of Shaded Region

= Area of Triangle - Area of Three sectors

=

(49 \sqrt{3} - \frac{49\pi}{2} ) {cm}^{2}(493−249π)cm2