The area of an equilateral triangle is 49 root 3cm2 Taking each angular point 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 the portion in the triangle not included in the circles
Answers
◀ HEY THERE!◀
◀ Question: ◀
→ The area of an equilateral triangle is 49√3 cm² Taking each angular point 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 the portion in the triangle not included in the circles ?→
◀ Method of Solution: ◀
→ Let the Side of Equilateral Triangle be a cm.
Then,→ Area of Equilateral Triangle =√3/4a² →
→ Given: Area of Equilateral Triangle= 49√3 cm²
Substitute the Given Value in Formula!
→Area of Equilateral Triangle = 49√3 cm²→
⇒ √3/4 a² = 49√3
⇒ a²/4= 49
⇒ a² = 49×4
⇒ a² = 196
⇒ •°• a = 14
Thus, The Length of each side of Circle measure is 14 cm (Diameter)
→ Therefore, Radius of each Circle = 7cm
[Area of Sector = ∅/360×πr²]
→ According to the Question's Statement!
Required Area = (area of ∆ABC) - 3(area of Sector)
⇒ 49√3 - 3[∅/360×22/7×(7)×(7)
⇒ 49√3 - 77/3 ×3 cm²
⇒ 49√3 - 77cm²
⇒ 7.87 cm²
◀ Hence, Area of Shaded Portion = 7.87 cm².◀
Refer to attachment
⚡⚡Dhruv⚡⚡⚡⚡
