Answer:
7182.6 m²
Explanation:
The area of the running track can be split into two shapes:
- A circle with radius 27m (There are 2 half circles that can be combined to form 1 full circle)
- A rectangle with 1 directly given side length, 90.6m
First, find the area of the circle:
A = πr² Plug in the given value, r.
A = π(27)² Square 27.
A = 729π Since the problem wants an exact value, simplify the equation.
A ≈ 2290.2
Now for the rectangle:
The rectangle has a missing side so the area can't be solved for just yet.
As you can see, the missing length's sides are also the diameters of the semicircles.
So, the missing side length is 2r.
2r = 2(27) = 54m
A = L · W Plug in the known values into the equation.
A = 54 · 90.6 Multiply to find the area.
A = 4892.4
Now that both shapes' areas are known, add both to get the area of the running track:
2290.2 + 4892.4 = 7182.6m²
The area of the running track rounded to 1 DP (decimal point) is 7182.6m².