2006-06-19 18:02:52 · 5 answers · asked by ais 1 in Science & Mathematics ➔ Mathematics
There are 5 bilateral triangles (equal size) or 10 right angled triangles (equal size) are in the pentagan. The angle of one bilateral triangle at the centre of the circle is 72 degree (360/5=72) and of one right angled triangle is 36 degree (72/2=36). Then one side of pentagan = 2*25*sin36 = 29.38926261 cm (the radius of the circle = 25 cm). The circumference of the pentagon = 5*(2*25*sin36) = 146.95 cm.
Area of one bilateral triangle = 0.5*height*base. Base = 2*25*sin36. Height = 25*cos36. Then area of one bilateral triangle = 0.5*(2*25*sin36)*(25*cos36) = 297.2051613. Then total of 5 bilateral triagles in the pentagan (Area of the PENTAGAN) = 5*0.5*(2*25*sin36)*(25*cos36) = 1486.03 sq.cm
2006-06-19 19:46:27 · answer #1 · answered by K.J. Jeyabaskaran K 3 · 0⤊ 0⤋
Divide the pentagon into 5 equal sized triangles. Each triangle will have two vertices's on the outer edge of the circle, and the last vertex will be at the center of the circle.
These 5 triangles will all be of equal size, and will have the following properties. Since 360degrees/5 triangles = 72degrees/triangle the vertex at the center will have an angle of 72 degrees. What follows is: (180 - 72) / 2 = 54, so each triangle will have two 54 degree angles, and one 72 degree angle.
Then use the law of cosines or law of sines to calculate the length of the base of the triangle that forms the pentagon multiply by 5, that will give you the circumference. Then divide the triangle into two right triangles so that you can calculate the area as 1/2 b*h. Then with that area multiply by 10 (because you will have 10 slices in your total pentagon), and that will give you the total area of the pentagon.
Hint: When you get the area of the pentagon it will be slightly less than Pi*25^2.
2006-06-20 01:20:24 · answer #2 · answered by unbound v 1 · 0⤊ 0⤋
Area of Circle (Pi*r2) = (3.14X 25X25)
Area of Pentagon (5*1/2 b*h) =5*(1/2 *25*Cos 54 * 25*Sin 36)
2006-06-20 01:18:56 · answer #3 · answered by Rohit 2 · 0⤊ 0⤋
If the unit of measurement is centimetres, the area would be 741.85 cm squared, and the "perimeter" of the pentagon would be 146.9 cm.
2006-06-20 01:29:32 · answer #4 · answered by Mujeeb A 1 · 0⤊ 0⤋
the circumference is 150.86 cm
the area is 1486.02 cm^2
If you want to know the solution I will be ready to help
2006-06-20 01:13:05 · answer #5 · answered by mohit 2 · 0⤊ 0⤋