A square piece of brown paper has side length 14. Two circle quadrants are inscribed inside the circle in order to form a green leaf as shown.
Find the area of the green leaf
Use the approximation, π = 7 2 2 .
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Good clear explanation.
From the picture above we can conclude that,
4 1 Circle Area - Triangle Area = 2 1 Leaf Area
( 4 1 × 7 2 2 × 1 4 2 ) − ( 2 1 4 × 1 4 ) = 2 1 Leaf Area
1 5 4 − 9 8 = 2 1 Leaf Area
5 6 = 2 1 Leaf Area
1 1 2 = Leaf Area
Sorry if this is a dumb question, but how do you make the assumption that the area is a quarter of a circle? Is this just self-evident, and I cannot see it? Thanks.
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Well i make The asumption so people won't confused was it a quarter or not ?
And it was on purpose
The area of the green leaf = 2(the area of the sector - the area of the triangle) = 2((phi/4) . 14.14 - 14.14/2) = 112
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We can see that the area of the leaf will be: ar(sqraure) − ar(remaining brown paper) . And;
ar(remaining brown paper) = 2 × ( ar(sqraure) − ar(quadrant) = 2 × ( 1 4 2 − 4 π 1 4 2 ) = 2 × ( 1 9 6 − 1 5 4 ) = 8 4 units 2
Therefore, ar(leaf) = 1 9 6 − 8 4 = 1 1 2 units 2