Question

Of segments CDF and CED, which of the segments has a greater area based on the given information? Justify with your work.(Do not use sin)

Circle A has radius 10m and m angle CAD=90 degrees
Circle B has radius 12m and m angle CBD=60degrees

Answer 1

for 1 st

area of segment CAD=90/360×π×10²=78.54m²

for second

area of segmentBCD=60/360×π×12²=75.4m²

so

CAD has greater area

Answer 2

• Segment CED has greater area

Explanation:

Circle A

Area of ΔCAD, right triangle:

• A = 1/2*10*10 = 50 m²

Area of the sector CAD:

• A = 1/4*π*10² = 78.54 m²

Area of segment CED:

• A = 78.54 - 50 = 28.54 m²

Circle B

Area of ΔCBD, equilateral triangle:

• A = √3/4*12² = 62.36 m²

Area of sector CBD:

• A = 1/6*π*12² = 75.40 m²

Area of segment CFD:

• A = 75.40 - 62.36 = 13.04 m²

Compare the areas of the segments:

• CED = 28.54 > CFD = 13.04