Class 10 [CBSE]
Need steps too… pls

(a) 2058 m2

Step-by-step explanation:

This track can be broken down into 4 components

A positive space rectangle and negative space rectangle in the middle.

A positive space circle, and negative space circle, due to there being 4 semicircles total at the end of each of the aforementioned rectangles.

Now we have to find the dimensions for all these shapes by simply looking at the image:

The total height is 56m (42m+7m+7m), that means Positive circle has a radius of 28m (56m diameter/2 = 28m radius).

The height for the negative space within the track is 42m, thus negative circle has a radius of 21m (42m diameter/2 = 21m radius)

Now for the rectangles:

Total length is 126m, and since we already found the diameter/radius of those semicircles, we can do simple subtraction to find the length of the rectangles: 126m-56m=70m.

Finding the height of both rectangles is easy, its the same as the circles:

Total height is 56m and negative space height is 42m.

Now we use those dimensions we found to calculate the area of all the shapes.

Positive circle area = (22/7)*(56m^2)=2464m2

Negative circle area = (22/7)*(42m^2)=1386m2

We now subtract the negative area from the positive area and we get a total circle area of 2464m2-1286m2=1078m2

Positive rectangle area = 56m*70m=3920m2

Negative rectangle area = 42m*70m=2940m2

Like we did with the circles, we subtract: 3920m2-2940m2=980m2

To finally find the total area of the tracks we add both areas we found together: (1078m2+980m2=2058m2)

So there's our answer!

P.S. This took a long time to solve so I hope it's appreciated :)

35-60 students are taking math.