Geometry Problem , can you help me

B and Z are on circle S. The diameter of circle S is 26, and the measure
of angle BSZ = 118o. What is the area of the sector created by arc BZ?
A. 4524.78
B. 118
C. 2262.39
D. 174.03
and explaination too if it isnt too much to ask

I can't remember the actual formula, but I set up an equations using proportions and found the answer to be D.

A circle is made of 360 degrees.

so, (total area)/(360 degrees) = (Area of sector)/(118 degrees)
Solve for area of sector:
(Area of Sector) = (total area)(118 degrees)/(360 degrees)

to find total area = (pi)(r^2)

Total Area = (3.14159)(13^2)
Total Area = 530.93

Plug this into the area of a sector formula:
(Area of Sector) = (total area)(118 degrees)/(360 degrees)
(Area of Sector) = (530.93)(118 degrees)/(360 degrees)

(Area of a Sector) = 174.03

TA-DAH!!

d

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Ok,
a sector is a part of s circle, we can find it be recognizing that the central angle is the part of the whole, being 360 degrees, so a whole circle is 360/360PI r^2, got it?

your sector will be 118/360 * pi * 13^2 (the radius is 13 because the diameter is 26)

sound good?
good luck!

the area of a circle πr^2

the area of a section of circle is ( arc measure/ 360) (π r^2)

(118/360) (π) (13^2)

174.03

Area = 118/360 * Total area of the circle

It's (d)