The area of an equilateral $Δ A B C$ 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 triangle. Find the area of the shaded region. $(π = 3.14, \sqrt{3} = 1.73205)$ [4 MARKS]

Open in App

Solution

Concept: 2 Marks
Application: 2 Marks

Area of shaded region = area of $Δ A B C$ - 3 (Area of sector BPR)

Let 'a' be the side of the equilateral $Δ$ ABC.

$\frac{a^{2} \sqrt{3}}{4} = 17320.5$

$a = 200 c m$

Radius of the circles
$= \frac{1}{2} \times a = 100 c m$

$∴$ Required area
$= 17320.5 - 3 [\frac{60}{360} \times π \times 100^{2}]$

$= 1620.5 c m^{2}$

Suggest Corrections

Similar questions

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.
$(U s e π = 3.14 a n d \sqrt{3} = 1.73205)$

Q. The area of an equilateral

Δ

ABC is 17320.5

c m^{2}

. A circle is drawn taking the vertex of the triangle as centre. The radius of the circle is half the length of the side of triangle. Find the area of the shaded region in

c m^{2}

. (Use

π = 3.14, \sqrt{3} = 1.73205

)

Join BYJU'S Learning Program

The area of an equilateral ΔABC is 17320.5 cm2 with each vertex of the triangle as centre a circle is drawn with radius equal to half the length of the side of triangle. Find the area of the shaded region. (π=3.14,√3=1.73205) [4 MARKS]

Concept: 2 Marks Application: 2 Marks Area of shaded region = area of ΔABC - 3 (Area of sector BPR) Let 'a' be the side of the equilateral ΔABC. a2√34=17320.5 a=200 cm Radius of the circles =12×a=100 cm ∴ Required area =17320.5−3[60360×π×1002] =1620.5 cm2

The area of an equilateral $Δ A B C$ 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 triangle. Find the area of the shaded region. $(π = 3.14, \sqrt{3} = 1.73205)$ [4 MARKS]