Home
Class 10
MATHS
In figure arcs are drawn by taking verti...

In figure arcs are drawn by taking vertices `A`, `B` and `C` of an equilateral triangle of side `10` `cm` , To intersect the sides `BC`, `CA` and `AB` at their respective mid- points `D`, `E` and `F`. Find the area of the shaded region. (use `pi = 3.14`)

Text Solution

Verified by Experts

Since, ABC is an equilateral triangle.
`:. angleA = angleB = angleC = 60^(@)`
and AB = BC = AC = 10cm
So, E, F and D are mid - points of the sides .
`:.` AE = EC = BD = BF = FA = 5cm
Now, area of sector CDE = `(thetapir^(2))/(360)=(60 xx 3.14)/(360)(5)^(2)`
= `(3.14xx25)/(6)=(78.5)/(6)=13.0833cm^(2)`
`:.` Area of shaded region = 3 (Area of sector CDE)
= `3xx13.0833`
= `39. 25cm^(2)`
Promotional Banner

Topper's Solved these Questions

  • AREAS RELATED TO CIRCLE

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer Type Questions|20 Videos

  • AREAS RELATED TO CIRCLE

    NCERT EXEMPLAR ENGLISH|Exercise Very Short Answer Questions|14 Videos

  • ARITHMETIC PROGRESSIONS

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer Type Questions|10 Videos

Similar Questions

Explore conceptually related problems

In the given figure, find the area of the shaded region [Use pi=3. 14]

In figure , AB is a diameter of the circle, AC = 6cm and BC = 8cm . Find the area of the shaded region . (use pi= 3.14 )

In Fig. an equilateral triangle A B C of side 6 cm has been inscribed in a circle. Find the area of the shaded region. (Take pi=3. 14 )

A circle is inscribed in an equilateral triangle A B C of side 12 cm, touching its sides (Figure). Find the radius of the inscribed circle and the area of the shaded part.

In Figure , O is the centre of the circle with AC = 24 cm, AB = 7 cm and /_BOD = 90° . Find the area of the shaded region. [Use pi = 3·14]

A circulare arc has been with vertex of an equilateral triangle of side 12 cm. The radius of arc is 6 cm. A sector of circle of radius 6 cm is cut from the triangle OAB. Find the area of the shaded region

The given figure shows an equilateral triangle ABC whose each side is 10 cm and a right-angled triangle BDC whose side BD = 8 cm and angleD=90^(@) . Find the area of the shaded portion.

In Figure, A B C is an equilateral triangle inscribed in a circle of radius 4 cm with centre O . Find the area of the shaded region.

In figure, arcs have been drawn of radius 21 cm each with vertices A , B , C and D of quadrilateral ABCD as centres . Find the area of the shaded region.

The given figure shows a square ABCD of side 20 cm. Semicircle are drawn with each side of the square as diameter. Find the area of the shaded portion. (Use pi = 3.14 )