Question

Please help me! How do I find the area of the shaded region in the circles?

Answer 1

ok, so i've never done this before, but i think i know how you do it. So first, find out the area of the whole triangle place in the circle shown on the diagram. Then, the area in the triangle that's not purple is what you need to subtract from the whole piece, i hope this helps

Explanation:

Answer 2

Explanation:

10a)

The formula for determining the area of a sector is expressed as

Area = #/360 × πr^2

From the diagram given,

# = π/3. We would convert π to degrees. 2π = 360 degrees. It means that π = 360/2 = 180 degrees. Therefore

π/3 = 180/3 = 60 degrees.

r = 10

Area of sector = 60/360 × 3.14 × 10^2 = 52.33 cm^2

Area of the triangle formed can be determined by the formula,

Area = 1/2abSinC

From the triangle,

a = 10,

b = 10

C = π/3 = 60 degrees. Therefore,

Area = 1/2 × 10 × 10 × Sin60 = 50 × 0.8660

Area of triangle = 43.3 cm^2

Therefore, area of the shaded region would be

53.3 - 43.3 = 10 cm^2

10b) looking at the diagram,

# = 135 degrees

r = 12

Area of sector = 135/360 × 3.14 × 12^2 = 169.56 cm^2

Area of the triangle = 1/2 × 12 × 12 × Sin 135 = 1/2 × 144 × 0.7071 = 50.9 cm^2. Therefore, the area of the shaded region would be

169.56 - 50.9 = 114.66 cm^2