Small Leaf, Big Problem

Geometry Level 2

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 = 22 7 \pi = \dfrac{22}{7} .


The answer is 112.

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3 solutions

Sravanth C.
Feb 10, 2016

We can see that the area of the leaf will be: ar(sqraure) ar(remaining brown paper) \text{ar(sqraure)} - \text{ar(remaining brown paper)} . And;

ar(remaining brown paper) = 2 × ( ar(sqraure) ar(quadrant) = 2 × ( 1 4 2 π 1 4 2 4 ) = 2 × ( 196 154 ) = 84 units 2 \text{ar(remaining brown paper)} = 2\times (\text{ar(sqraure)} - \text{ar(quadrant)}\\=2\times\left(14^2-\dfrac{\pi 14^2}4\right)\\=2\times(196-154)=84\text{ units}^2

Therefore, ar(leaf) = 196 84 = 112 units 2 \text{ar(leaf)} = 196-84=\boxed{112}\text{ units}^2

Moderator note:

Good clear explanation.

Jason Chrysoprase
Feb 10, 2016

From the picture above we can conclude that,

1 4 \frac{1}{4} Circle Area - Triangle Area = = 1 2 \frac{1}{2} Leaf Area

( 1 4 × 22 7 × 1 4 2 ) ( 14 × 14 2 ) = (\frac{1}{4} \times \frac{22}{7} \times 14^2) - (\frac{14 \times 14}{2}) = 1 2 \frac{1}{2} Leaf Area

154 98 = 1 2 154 - 98 = \frac{1}{2} Leaf Area

56 = 1 2 56 = \frac{1}{2} Leaf Area

112 = 112 = 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.

Drex Beckman - 5 years, 3 months ago

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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

Jason Chrysoprase - 5 years, 3 months ago
Rab Gani
Jul 30, 2020

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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