Home
Class 10
MATHS
The area of an equilateral triangle is 1...

The area of an equilateral triangle is `100sqrt(3)cm^(2)`. Taking each vertex as centre, a circle is described with radius equal to half the length of the side of the triangle, as shown in the figure. Find the area of that part o the triangle which is not included in the circles.
[Take `pi=3.14` and `sqrt(3)=1.732`]

Text Solution

Verified by Experts

Let each side of the triagnle be a cm. Then
area of the triangle `=((sqrt(3))/4a^(2))cm^(2)`.
`:.(sqrt(3))/4a^(2)=100sqrt(3)impliesa^(2)400impliesa=20`.
Thus, the length of each side of `DeltaABC` is 20 cm
`:.` radius of each cirlce `=10cm`
Required area
`=("area of" DeltaABC)-3("area of a sector with" r=10cm, theta=60^(@))`
`=(100sqrt(3)-3xx3.14xx10xx1060/360)cm^(2)`
`={(100xx1.732)-157}cm^(2)=(173.2-157)cm^(2)=16.2cm^(2)`
Hence the area of the required parts is `16.2cm^(2)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

The area of an equilateral triangle with side 2sqrt3 cm is

The area of an equilateral triangle is 1732.05cm^(2) .About each angular point as centre,a circle is described with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles.(Use pi=3.14) .

The area of an equilateral triangle ABC is 17320. 5" "c m^2 . With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region. (U

The area of an equilateral triangle is 4sqrt(3)cm^(2). The length of each of its sides is

The area of an equilateral triangle is 49sqrt(3) cm^(2) . Find its side (in cm).

The area of an equilateral triangle is 4sqrt3 cm^(2) . The length of each of its sides is

The area of the equilateral triangle is 20sqrt3cm^(2) whose each side is 8 cm.