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

69 sqm

To find the area of the running track, we need to subtract the area of the inner rectangle (gymnasium) from the area of the outer rectangle (including the track).

First, let's find the area of the outer rectangle:
- Length = length of gymnasium + 2 times the width of the track (since it runs all around)
- Width = width of gymnasium + 2 times the width of the track

Length of the outer rectangle = 50m + 2(2.5m) = 50m + 5m = 55m
Width of the outer rectangle = 30m + 2(2.5m) = 30m + 5m = 35m

Now, let's find the area of the inner rectangle (gymnasium):
Area of the inner rectangle = length of gymnasium * width of gymnasium = 50m * 30m = 1500m²

Finally, we can calculate the area of the running track by subtracting the area of the inner rectangle from the area of the outer rectangle:
Area of the track = Area of the outer rectangle - Area of the inner rectangle
= (55m * 35m) - 1500m²
= 1925m² - 1500m²
= 425m²

Therefore, the area of the running track is 425 square meters.