Question

please answer the following ...i will mark as brainliest..need explanation

Answer 1

Answer:

(1) 9√3 ( 1 + √3 ) / π²

Step-by-step explanation:

Let R be the radius.

The circumference of the circle is 3 + 4 + 5 = 12, so

2πR = 12  =>  R = 6/π.

The radii to the vertices divide the triangle into three isosceles triangles.  Each of these triangles has area

(1/2) × R² × sin( the angle at the centre of the circle )

= ( 18 / π² ) × sin ( the angle at the centre of the circle )

The angle subtended at the centre by the length 3 arc is (3/12)×360° = 90°.

The angle subtended at the centre by the length 4 arc is (4/12)×360° = 120°.

The angle subtended at the centre by the length 5 arc is (5/12)×360° = 150°.

Adding together the areas of the three smaller triangles, the area of the full triangle is then...

( 18 / π² ) × ( sin 90° + sin 120° + sin 150° )

= ( 18 / π² ) × ( 1 + sin 60° + sin 30° )

= ( 18 / π² ) × ( 1 + √3/2 + 1/2 )

= ( 18 / π² ) × ( ( 3 + √3 ) / 2 )

= ( 9 / π² ) × ( 3 + √3 )

= 9 ( 3 + √3 ) / π²

= 9√3 ( 1 + √3 ) / π²

Answer 2

by using concept of properties of triangles

answer is 1 option