The official distance between home plate and second base in a baseball diamond is 120 ft. Find the area of the official ball diamond and the distances between the bases. (The official ball diamond is in the form of a square.)
2nd to home is the diagonal of the square ... equal to the edge times √2
area = (diagonal^2) / 2
inter-base distance = diagonal / √2
To find the area of the official ball diamond, we need to know the length of each side of the square. Since the official distance between home plate and second base is equal to the length of one side of the square, we have:
Length of each side = 120 ft
To find the area of a square, we square the length of one side. In this case:
Area of the ball diamond = (Length of each side)^2 = (120 ft)^2 = 14,400 sq ft
Now, let's find the distances between the bases. A baseball diamond is divided into four equal sections, with the bases placed on the corners of the square. Since the square has sides of length 120 ft, the distance between each base is also 120 ft.
Distances between the bases:
- Home plate to first base: 120 ft
- First base to second base: 120 ft
- Second base to third base: 120 ft
- Third base to home plate: 120 ft
To find the area of the official ball diamond, we need to know the length of one side of the square. Since the distance between home plate and second base is given as 120 ft, we know that two sides of the square are each 120 ft.
To find the area of a square, we use the formula A = s^2, where A is the area and s is the length of one side.
In this case, the length of one side of the square is 120 ft, so the area of the diamond is A = 120 ft × 120 ft = 14,400 square feet.
Now let's calculate the distances between the bases.
Since the official ball diamond is a square, the distances between the bases are the same as the length of the sides of the square.
So, each side of the square is 120 ft, which means the distance between any two bases is 120 ft.