Question

A walking path at a local park is modeled on the grid below where the length of each grid square is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state, to the nearest square foot, the area of the walking path.

Answer 1

Answer:

The area of the walking path = 3,371 ft²

Explanation:

The complete Question is presented in the attached image to this solution

Note that the walking path consists of straight paths and curved paths.

The straight path is strictly squares, with 9 of them on both sides (top and bottom)

Area of the straight path = 18 × area of one square = 18 × 10² = 1800 ft²

For the curved path, note that their areas is the area between two semi circles.

Smaller semicircle has a radius of r = 20 ft.

Larger semicircle has a radius of R = 30 ft.

Area between the two semicircles = (Area of larger semicircle) - (Area of smaller semicircle)

= (πR²/2) - (πr²/2)

= (π×30²/2) - (π×20²/2)

= 785.4 ft²

But note that there are two of those curved paths, hence, area of the curved paths

= 2 × 785.4 = 1570.8 ft²

Total area of the walking path = (Area of straight path) + (Area of curved path)

= 1800 + 1570.8 = 3370.8 ft² = 3371 ft² to the nearest whole number.

Hope this Helps!!!