Examine the image of the track on the right. The first question in your Math Notebook asks, "What is the total area of the grassy area inside the track?"
The inside is composed of a rectangle and two semicircles.
The length and width of the rectangle are 84.39 meters and 73 meters, respectively.
The diameter of each semicircle is 73 meters.
Record these measurements in your Math Notebook and then continue to the question below.
A running track as given in the Math Notebook, with the height of the rectangle in the middle measuring 73 meters and its length measuring 84 point 3 9 meters. The width of the track is 9 point 7 6 meters.
A running track
3Points
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Question 2
Using the image of the track, find and label the areas of the rectangle and the two semicircles that make up the grassy area inside the track.
All units are in meters squared. Use begin mathsize 18px style 3.14 end style as an approximation for pi. Do not round your answer.
Hint: Area of a Rectangle= L x W
Area of a Semi-Circle= 3.14 cross times r squared divided by 2
To find the area of the rectangle, we use the formula:
Area of a Rectangle = Length x Width
Given that the length is 84.39 meters and the width is 9.76 meters, we can calculate the area:
Area of the Rectangle = 84.39 x 9.76
Area of the Rectangle = 824.0664 meters squared
To find the area of each semicircle, we use the formula:
Area of a Semicircle = (3.14 x r^2) / 2
Given that the diameter of each semicircle is 73 meters, we can calculate the radius:
Radius = Diameter / 2
Radius = 73 / 2
Radius = 36.5 meters
Now, we can calculate the area of each semicircle:
Area of each Semicircle = (3.14 x 36.5^2) / 2
Area of each Semicircle = (3.14 x 1332.25) / 2
Area of each Semicircle = 2092.8375 meters squared
To find the total area of the grassy area inside the track, we sum the area of the rectangle and the two areas of the semicircles:
Total Area = Area of Rectangle + 2 x Area of Semicircle
Total Area = 824.0664 + 2 x 2092.8375
Total Area = 824.0664 + 4185.675
Total Area = 5009.7414 meters squared
Therefore, the total area of the grassy area inside the track is 5009.7414 meters squared.