A gymnasium is 50m long and 30m broad. A running track 2. 5m wide runs all around it on the inside. Find the area of the track?
Are the ends semi-circles ?
If so, then the curved part must come in 15 m on each end, leaving a straight length of only 20 m for the rectangle.
outer area = rectangle of 20by30 + 1whole circle of radius 15
= 600 + π(225)
= (225π + 600) m^2
inner area = 25by20 + π(12.5^2)
= 500 + 156.25π
track area = 100 + 68.75π
To find the area of the track, we first need to calculate the area of the inner rectangle.
The length of the inner rectangle is the length of the gymnasium minus twice the width of the track:
Length of inner rectangle = 50m - 2 × 2.5m = 50m - 5m = 45m
The width of the inner rectangle is the breadth of the gymnasium minus twice the width of the track:
Width of inner rectangle = 30m - 2 × 2.5m = 30m - 5m = 25m
Now, we can calculate the area of the inner rectangle:
Area of inner rectangle = Length × Width = 45m × 25m = 1125m²
Since the track runs all around the inner rectangle, the area of the track is equal to the area of the outer rectangle (including the inner rectangle) minus the area of the inner rectangle:
Area of track = (Length of outer rectangle × Width of outer rectangle) - (Length of inner rectangle × Width of inner rectangle)
The length of the outer rectangle is the same as the length of the gymnasium:
Length of outer rectangle = 50m
The width of the outer rectangle is the same as the breadth of the gymnasium:
Width of outer rectangle = 30m
Now, we can calculate the area of the track:
Area of track = (50m × 30m) - (45m × 25m) = 1500m² - 1125m² = 375m²
Therefore, the area of the track is 375 square meters.
To find the area of the track, we need to subtract the area of the gymnasium from the area of the gymnasium including the track.
First, let's calculate the area of the gymnasium:
Area of the gymnasium = length × width = 50m × 30m = 1500m²
Next, we need to calculate the dimensions of the gymnasium including the track. Since the track runs all around the inside of the gymnasium, we need to add twice the width of the track to both the length and width of the gymnasium:
Length of the gymnasium including the track = length + 2 × track width
Width of the gymnasium including the track = width + 2 × track width
Plugging in the given values:
Length of the gymnasium including the track = 50m + 2 × 2.5m = 50m + 5m = 55m
Width of the gymnasium including the track = 30m + 2 × 2.5m = 30m + 5m = 35m
Now, let's calculate the area of the gymnasium including the track:
Area of the gymnasium including the track = (length including the track) × (width including the track) = 55m × 35m = 1925m²
Finally, to find the area of the track, we subtract the area of the gymnasium from the area of the gymnasium including the track:
Area of the track = Area of the gymnasium including the track - Area of the gymnasium
Area of the track = 1925m² - 1500m² = 425m²
Therefore, the area of the track is 425 square meters.