Based on the given dimensions, the perimeter of the figure is approximately 57.7 units.
How to find the perimeter of the figure
To find the perimeter of the figure composed of a parallelogram and a semicircle, calculate the sum of the lengths of all the sides.
Given that the dimensions of the parallelogram are 10 by 11, determine the lengths of its sides as follows:
The length of one side of the parallelogram is 10.
The width (or height) of the parallelogram is 11.
The perimeter of the parallelogram is calculated by summing the lengths of all four sides:
Perimeter of the parallelogram = 2 × (length + width)
Perimeter of the parallelogram = 2 × (10 + 11)
Perimeter of the parallelogram = 2 × 21
Perimeter of the parallelogram = 42
Now, calculate the perimeter of the semicircle.
Since a semicircle is half of a full circle, its perimeter is half the circumference of the corresponding circle.
The circumference of a circle is calculated using the formula:
Circumference = 2πr,
where π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, the diameter of the semicircle is 10 and radius is therefore 5
Perimeter of the semicircle ≈ 0.5 × Circumference of the circle with radius 5
Perimeter of the semicircle ≈ 0.5 × (2π × 5)
Perimeter of the semicircle ≈ 0.5 × (2 × 3.14159 × 5)
Perimeter of the semicircle ≈ 0.5 × (6.28318 × 5)
Perimeter of the semicircle ≈ 0.5 × 31.4159
Perimeter of the semicircle ≈ 15.70795
Now, find the total perimeter by summing the perimeter of the parallelogram and the perimeter of the semicircle:
Total Perimeter ≈ Perimeter of the parallelogram + Perimeter of the semicircle
Total Perimeter ≈ 42 + 15.70795
Total Perimeter ≈ 57.7
Rounded to the nearest tenth, the perimeter of the figure is approximately 57.7 units.