Question

1.
BTC
In Figure-8, find the area of the shaded region where a circular arc of
radius 7 cm has been drawn with vertex 0 of an equilateral triangle OAB
of side 14 cm as centre. (Use T = 22 and 13 = 1.73)
7 cm
213.11on?
2276132
A
14 cm
2​

Answer 1

Answer:

Area = 213.2 cm²

Step-by-step explanation:

Given, a= 14 cm, r= 7cm

Height of triangle = a√3/2

Angle of segment excluding triangle,Ф = 300°

Area = (Ф/360°)×π×r² + a×√3a/2×2

        = (300/360)×π×7² + 14×14×√3/4

        =49π×5/6 + 49×√3

        =128.3 + 84.9

Area=213.2 cm²        

Answer 2

Area of the shaded region (yellow colored) is 213.1 cm².

Step-by-step explanation:

In the figure attached,

Area of the shaded region = Area of triangle OAB + Area of circle O - Area of sector (colored in green)

Area of the equilateral triangle OAB = $\frac{\sqrt{3}}{4}(\text{Side})^{2}$

= $\frac{\sqrt{3}}{4}(14)^{2}$

= $49\sqrt{3}$ cm²

= 49×(1.73)

= 84.77 cm²

Area of the circle = πr²

= $(\frac{22}{7} )\times (7)^{2}$

= 154 cm²

Area of the sector (colored in green) = $\frac{\theta}{360}\times \pi r^{2}$

Since m(∠AOB) = 60°

So area of the sector = $\frac{60}{360}\times \pi (7)^{2}$

= $\frac{1}{6}\times (\frac{22}{7})\times (49)$

= 25.67 cm²

Now area of the shaded region (colored in yellow) = 84.77 + 154 - 25.67

= 213.1 cm²

Therefore, area of the shaded region (yellow colored) is 213.1 cm².

Learn more about the area of the sectors from https://brainly.in/question/2483458