Question

In the given figure a circle is inscribed in an equilateral triangle ABC of side 16 cm touching it's side find the radius of the inscribed circle and area of the shaded part

Answer 1

Answer:

where is the figure.

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Answer 2

radius of the inscribed circle = 8/√3 cm  , Area of shaded region = 43.8  cm²

Step-by-step explanation:

Triangle is Equilateral Triangle of side 16 cm

Area of Equilateral Triangle = (√3 / 4)(16)²

Let say r is radius of incircle

Then Area of Triangle

= (1/2) 16 * r  + (1/2)*16*r  + (1/2)16*r

= (3/2) * 16 r

(3/2) * 16 r  =  (√3 / 4)(16)²

=> (3/2) r = (√3 / 4) * 16

=>  (3/2) r = √3  * 4

=> 3r = 8√3

=> r = 8/√3

Area of shaded region = Area of Triangle - Area of circle

=  (√3 / 4)(16)² - π (8/√3)²

= 110.8  - 67

= 43.8  cm²

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