Question

In the fig. AB=16cm and BC=12cm.Calculate the area of the shaded region in the figure.​

Answer 1

Step-by-step explanation:

diagram 2016 basis for the calculation of area of shaded region in the figure is 18 cm

Answer 2

Answer: [96 – 16π] cm² or 45.76 cm²

Step-by-step explanation:

Given data:

AB = 16 cm

BC = 12 cm

To find: area of the shaded region

Solution:

Step 1:

We will first find the value for side AC.

Using the Pythagoras theorem for ∆ABC, we have

AC² = AB² + BC²

⇒ AC = √[AB² + BC²]  

⇒ AC = √[16² + 12²]

⇒ AC = √[400] = 20 cm

Step 2:

Now, we will find the area of ∆ABC.

∴ Area of ∆ABC = ½ * b * h = ½ * BC * AB = ½ *12*16 = 96 cm² ….. (i)

Step 3:

Here we will find the area of triangle for every side considering radius (r) of the circle as height.

∴ Area of the triangle = [1/2*16*r] + [1/2*12*r] + [1/2*20*r] = 24 r …….. (ii)

Equating (i) & (ii), we get

24 r = 96

⇒ r = 96/24 = 4 cm

Step 4:

In this step we will find the area of the circle.

∴ Area of the circle = πr² = π * (4)² = 16π cm²

Step 5 :

Thus,  

The area of the shaded region is given as,  

= [Area of ∆ABC] – [Area of the circle]

= [96 – 16π] cm² or 45.76 cm²