Can someone please break this down for me.

Given an oval track in the shape of a 48 m by 96 m rectangle with semicircular ends, you want the length of the track and the area enclosed.

Track Length

If you remove the rectangle, you see that what remains is a circle of diameter 48. The length of that circular portion of the track is the circumference of the circle:

C = πd

C = π(48 m) = 48π m ≈ 151 m

Added to that length are the two 96 m sides of the rectangle. So, the total length of the track is ...

track length = curved length + straight length

track length = 151 m + 2×96 m = 343 m

The length of the track is 343 meters.

Enclosed area

The area enclosed by the track includes the area of the circle we saw above, and the area of the rectangle.

The radius of the circular portion is half the diameter, or 24 m. Then the area is ...

A = πr²

A = π(24 m)² = 576π m² ≈ 1810 m²

The area of the rectangular portion is the product of length and width:

A = LW

A = (96 m)(48 m) = 4608 m²

The enclosed area is the sum of these areas:

enclosed area = area of circle + area of rectangle

enclosed area = 1810 m² +4608 m² = 6418 m²

The area enclosed by the track is 6418 square meters.

xero099 xero099 · Answer 2 · 2022-09-14T01:54:13+02:00

The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.

What is the perimeter and the area enclosed by the track?

In this problem we have a composite figure generated by a rectangle and two semicircles, of which we must determine its perimeter and area. The perimeter is the sum of the contour lengths of the semicircles and the rectangle and the enclosed area is the sum of areas of the two semicircles and a rectangle.

The perimeter of the composite figure is:

p = 2π · r + 2 · l

p = 2π · (24 m) + 2 · (96 m)

p ≈ 342.796 m

A = π · r² + l · (2 · r)

A = π · (24 m)² + (96 m) · (48 m)

A ≈ 6417.557 m²

The length (perimeter) of the track is approximately equal to 342.796 meters and the area enclosed by the track is approximately equal to 6417.557 square meters.

To learn more on perimeters and areas: https://brainly.com/question/11957651

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