Question

Omg please help with this

Answer 1

Answer: Area of the white region is 51.9 square cm

Explanation:

The given circle has a radius of 7cm.

Step 1: Calculate the area of complete circle

The area of circle is given as A=
`\pi r^(2)`

A=
`\pi (7)^(2)`

A=
`49 \pi`

Step 2: Calculate the area of a small segment of circle making 150 degrees.

The complete circle is of 360 degree

So, Area of a small segment of circle making 150 degrees will be,

A'=(150/360)
`49 \pi`

A'=64.14085

Step 3: Calculate the area of the white region

The small segment of the circle is made of a triangle in the blue and white region part

Therefore,

A'= 64.14085 = Area of triangle + Area of white region

Area of white region= 64.14085 - Area of a triangle

For the area of a triangle, two sides are equal and the radius of the circle

Therefore, It is an isosceles triangle

Area of triangle is given by = (1/2)(base)(height)

height = 7 cos (75)=1.8117

base = 2x7sin(75)=13.522

Note: Figure shown calculation of trigonometry.

Area of triangle is given by = (1/2)(1.8117)(13.522)=12.249

Area of white region= 64.14085 - Area of a triangle

Area of white region= 64.14085 - 12.249 =51.89185 square cm

Thus, the Area of the white region is 51.9 square cm