The formula for the area of a circle

The formula for the area of a circleElementary mathHS Math Geometry► Objective:To be able to find out the formula for the area of a circle► Procedure:(Review)●Review the meaning of “circumference” and the formula for the length of the circumference●Confirm the definition of π (circular constant)(Activity)●Prepare a graphing notebook(Or distribute a graphing paper)(Q) Draw a circle whose radius is 10 cm.(Q) “What is the area of this circle?”(As of this point, suppose that thestudents don’t know the formula forthe area of a circle.)→Students start counting the unit square.Teacher can expect several differentanswers. But those answers are not accurate.(Q) We are going to find the formula for thearea of a circle as well as we find anotherformulas for plane figures.●“We couldn’t get the area of a circle accurately. Why?”→Because unlike other plane figures, circle has a curve line.So far, we have been handling only polygons whose sides are all straight line.(Q) “Do you have any idea to make straight lines in this circle?”→We should cut it !(Q) “How should we cut it?” → along diameter, radius, etc.● First, cut this circle along the circumference.● Then cut this circle into 16 pieces along the radii.(Q) “Can you form another plane figure by using these pieces?” →Try it!(For example, square, rectangle, parallelogram, triangle, etc.)→This figure seems to be parallelogram (rectangle), but neither the upper line nor thelower line are straight line.

(Q) “If we cut this circle into small pieces, what shape can we form?”Cut and arrange again.The upper line and the lower line are almost to straight lines.(Q) “What will happen if we divide this circle into 100 pieces and arrange it?”→The shape will be closest to real parallelogram (rectangle).(Q) “Which part of the circle corresponds to the height (length)?”“Which part of the circle corresponds to the base (width)?”●height (length) → radius●base (width) → circumferenceThe formula for the area of a parallelogram = base×height(The formula for the area of a rectangle = length×width)(Write on the board)▲Let’s try to make the formula !▲The area of the circle= The area of the parallelogram (rectangle)=base × height (length×width)=radius×circumference÷2=radius×radius×2×π÷2(circumference=radius×2×π)=radius×radius×πTherefore,The formula for the area of a circle=radius×radius×π(Generalization)●Assessment(Exercise) Radius = 5cm.What is the area of this circle?The area of this circle = 5×5×π=25π(cm)

Another way of deriving the formula for the area of a circleCircle↔Triangle►ObjectiveTo be able to derive the formula for the area of a circle(Through the activity, students would be surprised at the unexpected result and derive the formulafor the area of a circle in an actual setting)►Procedure?Draw a circle whose radius is 3 cm.Put the double sides tape onthe illustration boardMake a hole at the center ofa circleRoll the yarn around acylindrical object and fix it tothe desk by using a rulerPut a yarn through the holeand fix it at the back by usingscotch tapeFrom the center of the circle,roll the yarn to the circumferenceCut the yarn from thecenter to the circumferenceFrom the circumference, arrange the cut yarnsfrom the longest yarn at the bottom to theshortest yarn at the top to create a straight lineWe can form a triangleThe formula for the area of a triangle1= × base × height2The formula for the area of a circle1= × circumffer ence×radius21= × diamiter × π × radius2= π × radius × radiusAteneo De Davao University – Regional Science Teaching Center