In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area
of the design (Shaded region).

In a circular table cover of radius 32 cm, a design is formed leaving an equilateral  triangle ABC in the middle as shown in Fig 12.24. Find the area of the  design

Asked by Pragya Singh | 1 year ago |  92

1 Answer

Solution :-

Radius of the circle = 32 cm

Draw a median AD of the triangle passing through the centre of the circle.

= BD = \( \dfrac{AB}{2}\)

Since, AD is the median of the triangle

AO = Radius of the circle = (\( \dfrac{2}{3}\)) AD

⇒ (\( \dfrac{2}{3}\)) AD = 32 cm

⇒ AD = 48 cm

In ΔADB,

Ncert solution class 10 chapter 12-17

By Pythagoras theorem,

AB= AD+BD2

⇒ AB= 482+\( ( \dfrac{AB}{2})^2\)

⇒ AB= 2304+\( \dfrac{AB^2}{4}\)

\( \dfrac{3AB^2}{4}\)= 2304

⇒ AB= 3072

⇒ AB= \( 32\sqrt{3}\) cm

Area of ΔADB = \( \dfrac{\sqrt{3}}{4}\) ×(32\( \sqrt{3}\))cm\(768 \sqrt{3}\)cm2

Area of circle = πR2 = (\( \dfrac{22}{7}\))×32×32 = \( \dfrac{22528}{7}\) cm2

Area of the design = Area of circle – Area of ΔADB

= (\( \dfrac{22528}{7}\) – \(768 \sqrt{3}\)) cm2

Answered by Abhisek | 1 year ago

Related Questions

Prove that the area of a circular path of uniform width hsurrounding a circular region of radius r is πh(2r + h).
 

Class 10 Maths Areas Related to Circles View Answer

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.
 

Class 10 Maths Areas Related to Circles View Answer

The outer circumference of a circular race-track is 528 m. The track is every­where 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre 
 

Class 10 Maths Areas Related to Circles View Answer

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of ₹25 per square metre (Use π = 3.14)

Class 10 Maths Areas Related to Circles View Answer

A path of width 3.5 m runs around a semi­circular grassy plot whose perimeter is 72 m. Find the area of the path.

Class 10 Maths Areas Related to Circles View Answer