Explanation with step(s):
- Let ABCDE be represented as the figure shown (Look at first image)
- Let the midpoint of the semicircle be known as "C" (First image)
Definition of Perimeter: The perimeter of any figure is the measure of the outer length of the boundary of the figure.
Since the diameter of the circle (BD) is inside the figure, we can remove it as it is not the outer length of the boundary of the figure. (Second image)
Determining the circumference of the semi-circle:
Now, let's determine the circumference of the semi-circle BCD. The circumference of a semicircle is expressed as 2πr/2
But we are given the diameter of the semicircle. Since the diameter of the semicircle is equivalent to twice times the radius, we can say that:
- ⇒ Circumference of semicircle = 2πr/2 = πd/2
Now, substitute the diameter in πd/2. Then, simplify the formula to determine the circumference of the semi-circle.
- ⇒ Circumference of semicircle = π(10)/2
- ⇒ Circumference of semicircle ≈ (3.14)(10)/2 [Measure of π: 3.14]
- ⇒ Circumference of semicircle ≈ (1.57)(10)
- ⇒ Circumference of semicircle ≈ (15.7)
Determining the perimeter of the rectangle:
- ⇒ Perimeter of rectangle: 2L + 2B
- ⇒ Perimeter of rectangle: 2(10) + 2(4)
As stated above, BD is excluded.
- ⇒ Perimeter of rectangle: 10 + 2(4)
- ⇒ Perimeter of rectangle: 10 + 8
- ⇒ Perimeter of rectangle: 18 cm
Determining the perimeter of the figure:
Add all the dimensions of the figure to determine the perimeter of the figure.
- ⇒ (15.7) + 18 cm
- ⇒ 33.7 cm
Therefore, the perimeter of the figure is 33.7 centimeters.
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