Question

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

Answer 1

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`