Find the area of the shaded region in the figure where the circle of radius 6 CM has been drawn with the vertex O of an equilateral triangle ABC of side 12 CM?

Question

Answer

Answer

Hey I can't use mathematical sign so it looks little difficult but hope u understand ..

OAB=equilateral triangle
so /_LOP= 60'(@) and side =12cm

now, required area =ar(circle)-ar(sector) +ar(ABC)-ar(sector)

=pie(r)^2 - pie(r)^2@/360+ root3 (side)^2/4 - pie(r)^2@/360

=3.14 ×6×6 - (3.14×6×6×60/360)+ 1.73×12×12/4 - (3.14×6×6×60/360)

3.14×36 + 1.73×36 - 2(3.14×6)

=113.04+62.28 - 37.68

shaded area =137.64cm^2

Answer

**Problem Statement:**

We are given an equilateral triangle ABC with side length 12 cm. A circle with radius 6 cm is drawn with the vertex O of the triangle as its center. We need to find the area of the shaded region in the figure.

**Solution:**

To find the area of the shaded region, we need to subtract the area of the equilateral triangle from the area of the circle.

**Step 1: Find the area of the equilateral triangle ABC**

An equilateral triangle has three equal sides and all angles measuring 60 degrees. We can use the formula to find the area of an equilateral triangle:

Area = (√3/4) * s^2

where s is the length of a side of the triangle.

In this case, s = 12 cm.

Area = (√3/4) * (12 cm)^2
= (√3/4) * 144 cm^2
= (√3/4) * 144 cm^2
= (√3/4) * 144 cm^2
= (√3 * 144 cm^2) / 4
= (√3 * 144 cm^2) / 4
= (√3 * 12 cm) * (√3 * 12 cm) / 4
= (√3 * 12 cm) * (√3 * 12 cm) / 4
= (√3 * 12 cm) * (√3 * 12 cm) / 4
= (√3 * 12 cm) * (√3 * 12 cm) / 4
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= (√3

Answer

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