Question

find the area of the shaded region in the following quadrants ​

Answer 1

Answer:

a)  the shaded region will be

ar(quadrant) = 1/4pir2

ar( triangle) = 1/2bh

ar( shaded region ) = 1/4pir2-1/2bh = 67/7

Step-by-step explanation:

Answer 2

Answer:

a) 4.07

b) 4.57

Step-by-step explanation:

a) Given, base of the triangle,b = 2

Height of the triangle,h = 3

Radius of the sector,r = 3

Area of a right angled triangle, $A_1=\frac{1}{2}bh$

$A_1=\frac{1}{2}\times 2\times 3$

$A_1=3$

Area of the sector, $A_2=\frac{\theta}{360}\times \pi r^2$.

Angle of the sector is $90$°.

$A_2=\frac{90}{360}\times \pi \times(3)^2$

$A_2=7.06858$

Area of the shaded region, $A=A_2-A_1$

$A=7.06858-3$

$A=4.07$

Area of the shaded region is $4.07$.

b) Given, base of the triangle,b =4

Height of the triangle, h=4

Radius of the sector, r=4

Area of a right angled triangle, $A_1=\frac{1}{2}bh$

$A_1=\frac{1}{2}\times 4\times4$

$A_1=8$

Area of the sector, $A_2=\frac{\theta}{360}\times \pi r^2$

Angle of the sector is $90$°.

$A_2=\frac{90}{360}\times \pi \times (4)^2$

$A_2=12.566$

Area of the shaded region, $A=A_2-A_1$

$A=12.566-8$

$A=4.566$

Area of the shaded region is $4.566$.