The area of an equilateral triangle ABC 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 the triangle (See the given figure). Find the area of shaded region. [Use π = 3.14 and] plz answer this question....and plz tell me step by step......can anyone...help me..
Answers
say: ABC is an equilateral triangle.
as all angles equals 60°
Area of ΔABC = 17320.5
side= a
as we know √3/4.(side)² = 17320.5
(a)² = 17320.5 × 4/1.73205
(a)² = 4 × 104
a = 200 cm
Radius of the circles = 200/2 cm = 100 cm
Area of 1 sector = (60°/360°) × π r²
= 1/6 × 3.14 × (100)²
= 15700/3
Area of 3 sectors = 3 × 15700/3 = 15700
Area of the shaded region = Area of equilateral ΔABC - Area of 3 sectors
= 17320.5 - 15700
= 1620.5
Answer:
1620.5cm²
step by step explanation:
area of shaded region = area of the equilateral triangle - area of the three sectors (i)
therefore, area of the equilateral triangle = √3/4 × a² = 17320.5
therefore, √3/4 × a² = 17320.5
a² = 17320.5 × 4/√3
a² = 17320.5 × 4/1.73205 (√3=1.73205)
a² = 40000
a = 200
radius of the circle = 200/2 = 100cm
area of the first sector = 60/360 × 3.14 × (100) ²
= 1/6 × 3.14 × (100) ²
= 15700/3
area of the three sectors = 3 × 15700/3 = 15700
putting the values of area of the equilateral triangle and area of the three sectors,we get
area of the shaded region = 17320.5 - 15700
= 1620.5cm²