Answer:
3.9 in²
Step-by-step explanation:
The shape is constructed of 2 semicircles (with diameter of 6 in) inside a square. Therefore, to calculate the yellow region, subtract the area of the semicircles (which form a circle) from the area of the square, then halve the answer.
Area of a square = [tex]x^2[/tex] ([tex]x[/tex] is the length of one side)
Given:
⇒ area of the square = 6² = 36 in ²
Area of a circle = [tex]\pi r^2[/tex]
Diameter of a circle = 2r
(where r is the radius)
Given:
- diameter = 6 in ⇒ r = 3 in
⇒ area of the circle = [tex]\pi[/tex] × 3² = 9[tex]\pi[/tex] in²
Area of yellow region = (area of square - area of circle) ÷ 2
= (36 - 9[tex]\pi[/tex]) ÷ 2
= 3.9 in² (nearest tenth)
