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Veronika [31]
3 years ago
11

What is the area of a shaded region in the quarter circle radius 12​

Mathematics
1 answer:
garik1379 [7]3 years ago
3 0

Answer:

I guess that the shaded area is a quarter of a circle of radius 12 units.

Is easy to know that the area, will be equal to the quotient between the area of a circle of radius 12, and 4

We know that the area of a circle of radius R is:

A = pi*R^2

in this case, R = 12

pi = 3.14

Then:

A = 3.14*12^2 = 452.16

And a fourth of that is:

A/4 = (452.16)/4 = 113.04

The area of the shaded region is 113.04 square units

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In the circle below, DB = 22 cm, and m<DBC = 60°. Find BC. Ignore my handwriting.​
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Answer:

BC=11\ cm

Step-by-step explanation:

step 1

Find the measure of the arc DC

we know that

The inscribed angle measures half of the arc comprising

m\angle DBC=\frac{1}{2}[arc\ DC]

substitute the values

60\°=\frac{1}{2}[arc\ DC]

120\°=arc\ DC

arc\ DC=120\°

step 2

Find the measure of arc BC

we know that

arc\ DC+arc\ BC=180\° ----> because the diameter BD divide the circle into two equal parts

120\°+arc\ BC=180\°

arc\ BC=180\°-120\°=60\°

step 3

Find the measure of angle BDC

we know that

The inscribed angle measures half of the arc comprising

m\angle BDC=\frac{1}{2}[arc\ BC]

substitute the values

m\angle BDC=\frac{1}{2}[60\°]

m\angle BDC=30\°

therefore

The triangle DBC is a right triangle ---> 60°-30°-90°

step 4

Find the measure of BC

we know that

In the right triangle DBC

sin(\angle BDC)=BC/BD

BC=(BD)sin(\angle BDC)

substitute the values

BC=(22)sin(30\°)=11\ cm

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Step-by-step explanation:

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Step-by-step explanation:

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