Question

In the given figure, O is the centre of the circle.Find the area of shaded region,given that BC=4cm and AB=3cm

Answer 1

Hope it helps you....

Answer 2

Answer:

3.82 sq-cm

Step-by-step explanation:

To find the area of shaded region,given that BC=4cm and AB=3cm

As we know that angle in semicircle is 90°,thus ∆ABC is right triangle, with the help of Pythagoras Theorem we can find the value of hypotenuse(AC),which is Diameter of circle.

$AC = \sqrt{ {BC}^{2} + {AB}^{2} } \\ \\ = \sqrt{16 + 9} \\ \\ = \sqrt{25} \\ \\ AC= 5 \: cm$

Radius of circle OA =OC =2.5 cm

Area of semicircle:

$= \frac{1}{2} \pi {r}^{2} \\ \\ = \frac{1}{2} \times \frac{22}{7} \times \frac{5}{2} \times \frac{5}{2} \\ \\ = \frac{11 \times 25}{28} \\ \\ = 9.82 \: {cm}^{2}$

$(ar \triangle \: ABC)= \frac{1}{2} \times base \times height \\ \\ = \frac{1}{2} \times 3 \times 4 \\ \\ = 6 {cm}^{2}$

Area of shaded region:

Area of semicircle-Area of triangle

=9.82 - 6

=3.82 sq-cm

Hope it helps you.