[40 points]

find the area of the shaded region.
enter a decimal rounded to the nearest tenth.

a = __ cm^2

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- First find the area of the whole circle

The equation is :

πr^2

Substitute the radius in:

π(5)^2

Solve:

Area of full circle = 25π

(Note : leave this answer in terms of 'pi' so it is easier to handle

Next, find the area of the sector

The equation for this is:

(angle/360) x πr^2

Substitute the values in:

(80/360) x π(5)^2

Solve :

Area of sector = (50/9)π

Now, find the area of the triangle:

1/2 absinC

Substitute the values in:

1/2(5)(5) x sin(80) = 12.31009691

Subtract this answer from the area of the sector

Answer = 5.14319607

Subtract this from the area of the whole circle

Answer = 73.39662073

To the nearest tenth, that would be 73.4 cm^2

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The area of shaded region is 61.4cm²

Step-by-step explanation:

Convert ° to π :

(80/180)° × π

= (4/9)π

A = (1/2)×5²×[(4/9)π - sin(4/9)π]

= 17.14cm² (not shaded region)

Area of circle = πr²

A = π×5²

=25π cm²

Area of shaded = Area of circle - Area of not shaded region

A = (25π - 17.14)cm²

= 61.4cm² (near. tenth)