Question

ΔLMN is an equilateral triangle. LM = 14 cm.As shown in figure, three sectors are drawn with vertices as centres and radius7 cm.Find
(1) A (ΔLMN)
(2) Area of any one of the sectors.
(3) Total area of all the three sectors.
(4) Area of the shaded region.

Answer 1

Side of Equilateral Triangle, a = 14 cm
Angle of sector,
$\theta = 60 \degree$
radius of sector, r = 7 cm


Ans: (1)
Area of an equilateral triangle =
$\frac{ \sqrt{3} }{4} {a}^{2} \\ = > \frac{ \sqrt{3} }{4} \times {14}^{2} = 49 \sqrt{3} {cm}^{2}$

Ans: (2)
Area of a sector
$= \frac{\pi {r}^{2} }{360 \degree} \times \theta = \frac{\pi \times {7}^{2} }{360 \degree} \times 60 \degree \\ = > \frac{49\pi}{6} {cm}^{2}$


Ans:(3) Since, All sectors are of same measure :
Total Area of Three sectors :
3*Area of one sector
=>
$3 \times \frac{49\pi}{6} = \frac{49\pi}{2} {cm}^{2}$


4) Area of Shaded Region
= Area of Triangle - Area of Three sectors
=
$(49 \sqrt{3} - \frac{49\pi}{2} ) {cm}^{2}$

Answer 2

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