94,059 views
8 votes
8 votes
Frank needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 60-m-by-60-m square. Frank says the area is 2,052.00 m squared. find the area enclosed by the figure. Use 3.14 for pie. What error might Frank have made?

User Shahzad Akram
by
2.2k points

1 Answer

20 votes
20 votes

Final answer:

To find the area enclosed by the figure, calculate the area of the square and the areas of the two semicircles, and add them together. Frank's error might be that he only considered the area of the square and one semicircle, instead of both semicircles. The correct area is 3882.6 m².

Step-by-step explanation:

To find the area enclosed by the figure, we need to calculate the area of the square and the areas of the two semicircles and then add them together. The area of the square is calculated by multiplying its length and width, which is 60 m * 60 m = 3600 m².

Each semicircle has a radius equal to half the length of the side of the square, which is 30 m. The area of each semicircle is calculated using the formula (π * r²)/2, where π is approximately 3.14 and r is the radius. So the area of each semicircle is (3.14 * 30 m²)/2 = 141.3 m².

Adding the area of the square and the area of the two semicircles together, we get 3600 m² + 141.3 m² + 141.3 m² = 3882.6 m².

Frank's error might be that he only considered the area of the square and one semicircle, instead of both semicircles. The correct area enclosed by the figure is 3882.6 m².

User Greyshack
by
2.4k points