Question

in the given figure BC is diameter .if ab = 3 cm ,AC= 4 cm and angle A = 90 degrees find the area of shaded region (π=3.14)
​

Answer 1

Answer:

Step-by-step explanation:

Given

$AB=3\text{ cm}$

$AC=4\text{ cm}$

$\angle BAC=90^\circ$

Therefore

$BC=\sqrt{AB^{2}+AC^{2}}\\\\\Rightarrow{BC}=\sqrt{3^{2}+4^{2}}\\\\\Rightarrow{BC}=\sqrt{9+14}\\\\\Rightarrow{BC}=\sqrt{25}\\\\\Rightarrow{BC}=5\text{ cm}$

The Diameter of the circle $D=5\text{ cm}$

therefore radius of the circle $r=\frac{D}{2}=\frac{5}{2}=2.5\text{ cm}$

Area of the circle

$A_{1}=\pi\times{r^{2}=3.14\times(2.5)^{2}=19.625\text{ cm}^{2}$

Area of the triangle

$A_{2}=\frac{1}{2}\times\text{Base}\times{\text{Height}$

$\Rightarrow{A_{2}}=\frac{1}{2}\times{AB}\times{AC}\\\\\Rightarrow{A_{2}}=\frac{1}{2}\times{3}\times{4}\\\\\Rightarrow{A_{2}}=6\text{ cm}^{2}$

The area of shaded region

$A=A_{1}-A_{2}\\\\\Rightarrow{A}=19.625-6\\\\\Rightarrow{A}=13.625\text{ cm}^{2}$

Answer 2

Answer:

Ans 13.625

Step-by-step explanation:

Area of shaded region = area of right angle triangle -area of circle