[tex] {\bold{\red{\huge{\mathbb{QUESTION}}}}} [/tex]
The semicircle shown at left has center X and diameter W Z. The radius XY of the semicircle has length 2. The chord Y Z has length 2. What is the area of the shaded sector formed by obtuse angle WXY?
[tex]\bold{ \red{\star{\blue{GIVEN }}}}[/tex]
RADIUS = 2
CHORD = 2
RADIUS --> XY , XZ , WX
( BEZ THEY TOUCH CIRCUMFERENCE OF THE CIRCLES AFTER STARTING FROM CENTRE OF THE CIRCLE)
[tex]\bold{\blue{\star{\red{TO \: \: FIND}}}}[/tex]
THE AREA OF THE SHADED SECTOR FORMED BY OBTUSE ANGLE WXY.
[tex] \bold{ \green{ \star{ \orange{FORMULA \: USED}}}}[/tex]
AREA COVERED BY THE ANGLE IN A SEMI SPHERE
[tex]AREA = ANGLE \: \: IN \: \: RADIAN \times RADIUS[/tex]
[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]
Total Area Of The Semi Sphere:-
[tex]AREA = \pi \times radius \\ \\ AREA = \pi \times 2 = 2\pi[/tex]
Area Under Unshaded Part .
Given a triangle with each side 2 units.
This proves that it's is a equilateral triangle which means it's all angles r of 60° or π/3 Radian
So AREA :-
[tex]AREA = \frac{\pi}{3} \times radius \\ \\ AREA = \frac{\pi}{3} \times 2 \\ \\ AREA = \frac{2\pi}{3} [/tex]
[tex] \green{Now:- } \\ \green{ \: Area \: Under \: Unshaded \: Part }[/tex]
Total Area - Area Under Unshaded Part
[tex] Area= 2\pi - \frac{2\pi}{3} \\ Area = \frac{6\pi - 2\pi}{3} \\ Area = \frac{4\pi}{3} \: \: ans[/tex]
[tex] \red \star{Thanks \: And \: Brainlist} \blue\star \\ \green\star If \: U \: Liked \: My \: Answer \purple \star[/tex]
