Question

AXB is a semicircle AB is a diameter, AB = 12 AYB is a arc having measure 120 find the area of shaded rigion​

Answer 1

Answer:

$ar \: of \: semi \: circle = \pi \times 6 \times 6 \div 2 - \pi \times 6 \times 6 \div 3 =$

Answer 2

Given:

• AXB is a semicircle AB is a diameter, AB = 12

• AYB is a arc having measure 120

To Find:

• The area of shaded region​ .

Solution:

Diameter = 12 unit

Radius  $= \frac{12}{2} = 6\ unit$

Now,

AYB is an arc having 120°

Area of the semicircle =  $\frac{\pi \ r^2 }{2}$

                                       = $\frac{22}{2 \times 2} \times (6)^2$

                                     $= 56.52 \ square \ unit$

Thus, Area of the semicircle $= 56.52 \ square \ unit$

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

                                  $= \frac{22 \times (6)^2 \times 120^\circ }{7 \times 360^\circ}$                      

                                 $= 37.68 \ square \ units$

Thus, the area of the sector  $= 37.68 \ square \ units$

Area of the shaded region =$Area \ of \ the \ semicircle - Area \ of \ the \ sector$

                                             $= 56.52 - 37.68$

                                             $= 18.84 \ square \ units$

Hence, the area of the shaded region $= 18.84 \ square \ units$