VIEWS: 4 PAGES: 13 POSTED ON: 8/4/2012 Public Domain
Presented by MJ Lund If a circle has a circumference of C units and a radius of r units, then C = 2πr. If a circle has an area of A square units and a radius of r units, then A = πr2 r Example #1: Find the area of the shaded region 18 yd Solution: Plan: Area of square - Area of the circle Formulas: A = s2 – πr2 A = 502 - π182 A = 2500 - 324π sq yds 50 yd or A = 1482.12 sq yds. y x Example #2: (2,-5) 9 Find the area of a circle with the equation (x-2)2 + (y+5)2 = 81 •This is a circle whose center point is (2,-5) and whose radius is 9. •Therefore, A = π r2 and A = (π)(9)2 and so the A = 81π or about 254.5 sq units Area of a Sector What is a “sector”? A sector is a section of the circle bound by two radii and their intercepted arc. In simpler terms, the shape of a slice of pizza. sector Calculating the area of a sector Once again, you are confronted with another formula. Here is the area of a sector formula: mAB Area r 2 360 The formula calculates the total area of the circle first, then the formula takes the arc measure and divides by 360 to calculate the portion of the total area called a sector. Area of a sector example #3: Given the following information with the diagram, calculate the area of the sector. mAB Area r 2 360 120 Area 5 2 Plug in numbers for variables 360 1 A 5 cm Area 25 Simplified values 3 120 25 Area Multiplied 3 78.54 2 Area 26.18cm Final answer 3 B Calculating the area of a segment What’s a segment? A segment of a circle is a region bounded by a chord and its intercepted arc. Segment calculation process 1. Calculate the area of the sector. 2. Calculate the area of the triangle in the sector. 3. Subtract the area of the triangle from the area of the sector. Segment example #4: Given the following information with the diagram, calculate the area of the segment of the circle. mAB sector r 2 Area of sector formula A 360 90 sector 12 2 Plug in values for variables 360 1 sector 144 Simplified B 4 O 144 12 yd sector Multiplied 4 sector 36 113.1yd 2 Sector answer continue Segment example #4 continued: Now that you have calculated the sector, calculate the area of the triangle inside the sector. 1 A triangle b h Area of a triangle formula 2 1 The base and height are 12 because each triangle 12 12 represent radii of the circle. 2 1 Multiplied triangle 144 B 2 O triangle 72yd 2 12 yd Multiplied continue Segment example #4 concluded: The last stage is to subtract the area of the triangle from the area of the sector. segment sector triangle A segment 113.1yd 2 72yd 2 Plug in values segment 41.1yd 2 Final answer B O 12 yd Segment area = 41.10 square yds