Question

in the given figure ABC is diameter if a b is equal to 3 centimetres is equal 4 cm and angle is equal to 90 degree find the area of the shaded region​

Answer 1

Answer: $(6.25\pi-6)$ square cm

Step-by-step explanation:

Since, ∠ BAC = 90°     ( angle on the semi circle )

Thus, by the Pythagoras theorem,

$BC^2 = AB^2 + AC^2$

$BC^2 = 3^2 + 4^2 = 9 + 16=25$

$\implies BC = 5\text{ cm}$

Since, BC is the diameter of the given circle,

⇒ Radius of the circle = BC/2 = 5/2 = 2.5 cm,

Hence, the area of the given circle = $\pi (2.5)^2$

$=6.25\pi$ square cm

Now, the area of right triangle ABC = 1/2 × AB × AC = 1/2 × 3 × 4 = 6 square cm

Since, the area of the shaded region = Area of the circle - area of the triangle inside the circle

= $(6.25\pi - 6)\text{ square cm}$