· The area of an equilateral triangle ABC is 17320.5
cm'. 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. (Use a = 3.14 and
13 = 1.73205)
Answers
Since the triangle is equilateral, each of its angle will be equal to 60°
∴Area of the part of each circle which is inside the triangle will be = {60×π×(a/2)²}/360 = {π×(a/2)²}/6
And you can find length of each side of the triangle by using the formula (√3)a²/4 = Area of triangle ABC
∴ Area of the shaded region will be = Area of triangle ABC - [3×{π×(a/2)²}/6] = Area of triangle ABC - [{π×(a/2)²}/2]
Mark my answer as Brainliest
Follow me if I was helpful, you can ask me your math queries without any hesitation :)
Answer:
Area of shaded part is 1620.5cm²
Step-by-step explanation:
Area of triangleABC=17320.5
^3/4×s²=17320.5
s²=17320.5×4/^3
s²=17320.5×4/1.73205
s²=173205×4×100000/173205×10
s=^40000
s=200
1/2×Length of triangle=Radius of circle
1/2×200cm=Radius
Radius=100m
Area of circle inside triangle=60°/360°×3×πr²
=1/6×3×3.14×100×100
=1/2×314×100
=50×314
=15700
Area of shaded part=Area of triangle-Area of circle
Area of shaded part=17320.5cm²-15700cm²
Area of shaded part=1620.5cm²