Question

The vertices of a triangle lie on the circumference of a circle. If its sides are 2.5 cm, 6 cm, and 6.5 cm, what is the area of the circle (in cm2)?


options:

42.5625pie

42.25pie

10.5625pie

9pie

Answer 1

Answer:

42.5625pie

42.25pie

10.5625pie

9pie

Step-by-step explanation:

Answer 2

Answer:

The correct option is 10.5625 $\pi$

Step-by-step explanation:

Given data

Vertices of the triangle are 2.5 cm, 6 cm and 6.5 cm

the given vertices of a triangle are lie on the circumference of a circle  

Here we need to find area of the circle  

the vertices of the triangle are on the circumference of the circle  

⇒ then the circle is a Circumcircle of a Triangle  

⇒ radius of the circumcircle of the triangle (r) =  abc / 4Δ  

here a, b and c are sides of the triangle

         Δ is area of the triangle  

⇒ now find area of the triangle  

   ⇒ $\sqrt{s(s-a)(s-b)(s-c)}$      [ here s = (2.5+6+6.5)/ 2 = 7.5 ]

   ⇒ $\sqrt{7.5(7.5-2.5) (7.5- 6)(7.5- 6.5)}$  

   ⇒  $\sqrt{7.5(5) (1.5)(1)}$  

   ⇒  $\sqrt{(7.5)(7.5)}$  = 7.5 cm

⇒ radius of the circle r = (2.5 × 6 × 6.5) / 4(7.5)

                                      =$\frac{97.5}{30 }$ = 3.25 cm

⇒ Area of the circle = $\pi r^{2}$  = (3.25)(3.25) $\pi$  

                                           = 10.5625 $\pi$