Alex mounts the clock on a wood base with the shape shown at the right what is the area of the wood base
the composite figure is a square with a semicircle on top it
the square is 18 inches in length and 20 inches in height
whats the answer
To find the area of the wood base, we need to calculate the area of the square and the area of the semicircle, and then add them together.
1. Area of the square:
The formula to calculate the area of a square is A = side length * side length. Given that the side length of the square is 18 inches, we can calculate the area as:
A_square = 18 inches * 18 inches = 324 square inches.
2. Area of the semicircle:
The formula to calculate the area of a semicircle is A = (π * r^2) / 2, where r is the radius. In this case, the width of the square (20 inches) is also the diameter of the semicircle, so the radius is half of the width = 20 inches / 2 = 10 inches. Now we can calculate the area of the semicircle:
A_semicircle = (π * 10 inches * 10 inches) / 2 = (π * 100 square inches) / 2 = 50π square inches.
3. Total area of the wood base:
Finally, we add the area of the square and the area of the semicircle together to get the total area of the wood base:
A_wood base = A_square + A_semicircle = 324 square inches + 50π square inches.
So, the area of the wood base is 324 square inches plus 50π square inches.
To find the area of the wood base, we need to find the combined areas of the square and the semicircle.
1. Start by finding the area of the square:
The formula for the area of a square is side length squared (A = s^2).
In this case, the length of the side of the square is given as 18 inches.
So, the area of the square is A = 18^2 = 324 square inches.
2. Next, find the area of the semicircle:
The formula for the area of a semicircle is half the area of a full circle (A = 0.5 * π * r^2).
In this case, the radius (r) of the semicircle is equal to half the side length of the square, which is 18/2 = 9 inches.
So, the area of the semicircle is A = 0.5 * π * 9^2 = 0.5 * π * 81 = 40.5π square inches.
3. Finally, sum up the areas of the square and semicircle to find the total area of the wood base:
Total area = Area of square + Area of semicircle = 324 + 40.5π square inches.
Therefore, the area of the wood base is 324 + 40.5π square inches.