Question
What is the area of the rectangular Pentagon within a pothium 14 in long and a side 20 in long round the answer to the nearest inch
Answers
Answered by
GPT 3.5
To find the area of the rectangular pentagon, first find the area of the rectangle:
Area = length x width
Area = 14 in x 20 in
Area = 280 square inches
Then, since it is a pentagon, the corners need to be cut off. The best way to calculate the area of the cut off corners is to find the area of the semicircles with a diameter equal to the length of the corner.
The corners are each in the shape of a semicircle with a radius of 14/2 = 7 in.
Area of a circle = πr^2
Area of each semicircle = π(7)^2 / 2
Area of each semicircle ≈ 38.48 square inches
Total area of the two cut off corners = 38.48 in^2 x 2 = 76.96 square inches
Final area of the pentagon = Area of rectangle - Area of cut off corners
Final area = 280 in^2 - 76.96 in^2 ≈ 203.04 square inches
Therefore, the approximate area of the rectangular pentagon is 203 square inches.
Area = length x width
Area = 14 in x 20 in
Area = 280 square inches
Then, since it is a pentagon, the corners need to be cut off. The best way to calculate the area of the cut off corners is to find the area of the semicircles with a diameter equal to the length of the corner.
The corners are each in the shape of a semicircle with a radius of 14/2 = 7 in.
Area of a circle = πr^2
Area of each semicircle = π(7)^2 / 2
Area of each semicircle ≈ 38.48 square inches
Total area of the two cut off corners = 38.48 in^2 x 2 = 76.96 square inches
Final area of the pentagon = Area of rectangle - Area of cut off corners
Final area = 280 in^2 - 76.96 in^2 ≈ 203.04 square inches
Therefore, the approximate area of the rectangular pentagon is 203 square inches.