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28 votes
28 votes
Find the area of the shaded region. Use the pin button on the calculator. Round to the nearest whole number. 14 70°

User Giorgos Ath
by
2.5k points

1 Answer

13 votes
13 votes

Answer:

The area is approximately
588cm^2

Explanation:

Given

See attachment for figure

Required

The area of the shaded region

The shaded region is as follows:

  • A major segment
  • A triangle

First, calculate the area of the major segment using:


Area = (\theta)/(360) * \pi r^2

Where


r = 14


\theta = 360 - 70 =290

So, we have:


A_1 = (290)/(360) * 3.14 * 14^2


A_1 = 495.7711

Next, the area of the triangle using:


Area = (1)/(2)ab \sin C

Where


a=b=r = 14


C = 70^\circ

So, we have:


A_2 = (1)/(2) * 14 * 14 * sin(70)


A_2 = 92.0899

So, the area of the shaded region is:


Area = A_1 + A_2


Area = 495.7711 + 92.0899


Area = 587.8610


Area \approx 588

Find the area of the shaded region. Use the pin button on the calculator. Round to-example-1
User V H
by
2.7k points