Answer:
The shaded area is 314.2 cm²
Step-by-step explanation:
Here we note that the shape consists of two small circles and one larger circle
The diameter of the larger semicircle is subtended by the two smaller semicircles, the small semicircle closer to the left of the internal circumference of the larger semicircle is shaded one while the one on the right is without color,
Therefore,
Diameter of larger semicircle = 2 × 10 = 20 cm
Based on the diagram, the shaded area is observed to be;
Shaded area = Area of semicircle formed by larger diameter or 20 cm + Area area formed by the small semicircle close to the right of the internal circumference of the larger semicircle - Area area formed by the other smaller semicircle
Since the diameter and therefore the areas of the two small semicircles are equal, we have;
Shaded area = Area formed by the complete larger semicircle = Area of semicircle formed by larger diameter or 20 cm
∴ Shaded area = π·D²/4 = π×20²/4 = 100×3.142 cm² = 314.2 cm².
The area of the shaded region is 157.1 square centimeters and this can be determined by using the formula of the area of the semicircle.
Given :
The following steps can be used in order to determine the area of the shaded region:
Step 1 - First, determine the area of the smaller semicircle.
[tex]\rm A' = \dfrac{1}{2}\times \pi \times (5)^2[/tex]
A' = 39.275 square centimeter
Step 2 - Now, determine the area of the larger semicircle.
[tex]\rm A'' = \dfrac{1}{2}\times \pi \times (10)^2[/tex]
A'' = 157.1 square centimeter
Step 3 - So, the area of the shaded region is:
A = 157.1 + 39.275 - 39.275
A = 157.1 square centimeters
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https://brainly.com/question/1631786