Find the area of the shaded region if ABCD is a square of side 14 cm a...
Given:
- ABCD is a square of side 14 cm.
To Find:
- The area of the shaded region.
Approach:
1. Divide the shaded region into three parts: the square, and the two semicircles.
2. Calculate the area of each part.
3. Add the areas of the square and the two semicircles to find the total area of the shaded region.
Calculation:
1. Area of the Square:
- The side of the square is given as 14 cm.
- The area of a square is given by the formula: Area = side^2.
- Substituting the given value, we get: Area = 14^2 = 196 cm^2.
2. Area of the Semicircles:
- The diameter of each semicircle is equal to the side of the square, which is 14 cm.
- The radius of each semicircle is half the diameter, so the radius is 14/2 = 7 cm.
- The area of a semicircle is given by the formula: Area = πr^2/2, where π is a constant approximately equal to 3.14.
- Substituting the given values, we get: Area = 3.14 * 7^2/2 = 3.14 * 49/2 = 76.93 cm^2 (rounded to two decimal places).
- Since there are two semicircles, the total area of the two semicircles is 2 * 76.93 = 153.86 cm^2 (rounded to two decimal places).
3. Total Area of the Shaded Region:
- To find the total area of the shaded region, we add the area of the square and the area of the two semicircles.
- Total Area = Area of Square + Area of Semicircles = 196 + 153.86 = 349.86 cm^2 (rounded to two decimal places).
Answer:
- The area of the shaded region is approximately 349.86 cm^2.
Find the area of the shaded region if ABCD is a square of side 14 cm a...
Where is the shaded region given???
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