TS EAMCET 19-July-2022 Shift 2 Solved Paper

Let BC,AC and AB are a,b and c respectively.In △ABD,
G is the centroid and centroid divides the median in the ratio 2:1
AG=‌

2

3

×4=‌

8

3

In △ABG,‌‌‌

sin‌ π 6

BG

=‌

sin‌ π 3

AG

⇒‌‌‌

1

2BG

=‌

√3

2×‌ 8 3

⇒BG=‌

8

3√3

=‌

8√3

9

In △AGB,
⇒‌‌‌

1

2BG

=‌

√3

2×‌ 8 3

⇒BG=‌

8

3√3

=‌

8√3

9

In △AGB,
‌

π

6

+‌

π

3

+∠AGB=π⇒∠AGB=‌

π

2

∴ Area of △AGB=‌

1

2

×AG×BG
=‌

1

2

×‌

8

3

×‌

8√3

9

=‌

32√3

27

As the median divides the triangle in equal parts
Area of △ABC=3 (Area of △AGB)
=3×‌

32√3

27

=‌

32√3

9

sq. units
=‌

32

3√3

sq. units