SOLUTION: Jim doesn't like crust, so he cuts a triangular slice out of his pizza. The pizza is 18 inches in diameter. Point P is located in the center and points a and z are the outer edge.

Algebra ->  Surface-area -> SOLUTION: Jim doesn't like crust, so he cuts a triangular slice out of his pizza. The pizza is 18 inches in diameter. Point P is located in the center and points a and z are the outer edge.       Log On


   

Question 769201: Jim doesn't like crust, so he cuts a triangular slice out of his pizza. The pizza is 18 inches in diameter. Point P is located in the center and points a and z are the outer edge. With the slice removed, what is the remaining area of the pizza?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Hard to draw the figure in a reliable way, so describing.

C is the center point of pizza, P is a point on the edge, make an angle 120 degrees from P to another point M. In middle of P and M is point D.

CP is 18 inches
Triangle CDP is a 30-60-90 triangle and angle CDP is 90 degrees. Angle PCD is 60 degrees. Triangle is half of a equilateral triangle, so CD is 4&1/4 inches.

Use pythagorean theorem, DP=sqrt%289%5E2-%289%2F2%29%5E2%29
DP=%289%2F2%29sqrt%283%29

Area of the slice then is, since there are three triangles with the central angle of 120 degrees, 3%2A%289%2F2%29%28%289%2F2%29sqrt%283%29%29
Which is like %281%2F2%29%2ACD%2ADP AND THEN MULTIPLY BY 6.

Area of the original pizza was pi%2A9%5E2