Find the area 0f shaded region
Answers
Answer:
Perimeter = 13.2 cm (approx)
Area = 4.62 cm² (approx)
Step-by-step explanation:
The question on the page asks for the perimeter. The question as posted in Brainly asks for area. Let's do both, just to be safe.
Perimeter
The circumference of a circle is given by 2πr, where r is the radius.
AEB = half circumference of circle with diameter 2.8 cm
= π r, with r = 2.8 / 2 = 1.4 cm
= 1.4 π cm
BFC = half circumference of circle with diameter 1.4 cm
= π r, with r = 1.4 / 2 = 0.7 cm
= 0.7 π cm
CDA = half circumference of circle with diameter (2.8+1.4) cm = 4.2 cm
= π r, with r = 4.2 / 2 = 2.1 cm
= 2.1 π cm
The perimeter of the shaded region...
= AEB + BFC + CDA
= ( 1.4 + 0.7 + 2.1 ) π cm
= 4.2 π cm
≈ 13.2 cm (approx)
Area
The area of a circle is given by π r², where r is the radius.
area AEB = half area of circle with diameter 2.8 cm
= (1/2) π r², with r = 2.8 / 2 = 1.4 cm
= 0.98 π cm²
area BFC = half area of circle with diameter 1.4 cm
= (1/2) π r², with r = 1.4 / 2 = 0.7 cm
= 0.245 π cm²
CDA = half area of circle with diameter (2.8+1.4) cm = 4.2 cm
= (1/2) π r², with r = 4.2 / 2 = 2.1 cm
= 2.205 π cm²
The area of the shaded region...
= area CDA + area BFC - area AEB
= ( 2.205 + 0.245 - 0.98) π cm²
= 1.47 π cm²
≈ 4.62 cm² (approx)