Answer:
Total perimeter = 38 units.
Total area = 95 sq. units.
Step-by-step explanation:
See the attached figure.
a) The perimeter of the circular portion is one-fourth of the circumference of a full circle.
So, as the radius is 5 units, so the perimeter will be [tex]\frac{1}{4} (2\pi r) = \frac{22 \times 2 \times 5}{7 \times 4} = 7.857[/tex] units.
Therefore, the total perimeter will be (10 + 10 + 5 + 5 + 7.857) = 37.857 ≈ 38 units. (Answer)
b) The area of the circular portion is one-fourth of the area of a full circle.
So, area of the circular portion is [tex]\frac{1}{4}(\pi r^{2}) = \frac{22 \times 5^{2}}{4 \times 7} = 19.643[/tex] sq, units.
Therefore, the area of the total figure will be [(5 × 5) + (5 × 5) + (5 × 5) + 19.643] = 94.643 sq. units ≈ 95 sq. units. (Answer)
Perimeter of the given figure will be 38 units.
Given in the question,
Perimeter of a polygon = Measure of the circumference of the polygon
From the figure attached,
Perimeter of the figure = measure of the three straight lines + measure of the circumference of the quarter circle
Measure of linear sides = 5 + 10 + 10 + 5 = 30 units
Circumference of the quarter circle = [tex]\frac{1}{4}(2\pi r)[/tex]
= [tex]\frac{1}{2}(\pi )(5)[/tex]
= 7.85 units
Perimeter of the figure = 30 + 7.85
= 37.85
≈ 38 units
Therefore, perimeter of the given figure will be 38 units.
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