Answer:
- perimeter: 47.12 units
- area: 151.60 square units
Explanation:
You want the perimeter and area of a figure consisting of a 4 × 11 rectangle with semicircles attached to each straight edge.
Perimeter
If you trace the perimeter of the figure, you see you are tracing the circumference of a circle 4 units in diameter and the circumference of a circle that is 11 units in diameter. The circumference of a circle is given by ...
C = πd
so the total circumference is ...
C1 +C2 = π(4) +π(11) = π(4+11) ≈ 47.12 . . . . units
The perimeter of the figure is about 47.12 units.
Area
The area of two half-circles is the area of one whole circle of the same diameter. The area of a circle of diameter d is given by ...
A = (π/4)d²
The total area of the circles of diameters 4 and 11 is ...
A1 +A2 = (π/4)·4² +(π/4)·11² = (π/4)(4² +11²)
The area of the central rectangle is added to the areas of the semicircles. Its area is ...
A = LW
A = (11)(4)
Total
The area of the entire figure is the sum of the circle areas and the rectangle area:
total area = (π/4)(4² +11²) +(4)(11) ≈ 151.60 . . . . square units
The area of the figure is about 151.60 square units.
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Additional comment
You usually see the formula for the area of a circle as ...
A = πr²
Since r = d/2, we can express this using d as ...
A = π(d/2)² = π(d²)/(2²) = (π/4)d²
You may notice that a square that circumscribes the circle will have a side length of d, and an area of d². The fraction π/4 tells you the fraction of that enclosing square that is covered by the circle. This fact can help you estimate areas and volumes of circles and cylinders.