# Find the green shaded area? Relevance
• Anonymous
2 months ago

24 - (2.5)^2pimmmmmmm

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• I found it its next to the yellow circle

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• It's right there surrounding the yellow circle.

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• The way to find it would be to use the formula to find the area of the triangle and then to subtract from it the area of the circle. There is no direct way to find the green area on it's own.

• Puzzling
Lv 7
2 months agoReport

They said, "subtract from [the triangle] the area of the circle."

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• It's right there along the inside edges of the triangle.

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24 - 19.63 = 4.37

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• Hi Michelle,

I'm surprised by the number of people offering the same wrong answer. This question looks deceptively straight-forward.

The wrong answers are because either (or both):

A) At least one of the three sides of the triangle is not tangent to the circle, so the circle overlaps one or more sides.

B) This is not a right triangle.

This is clear because the circle (the incircle) that has the sides of a 6, 8, 10 right triangle as tangents has a diameter of 4 units.

In the non-right triangle with sides 8, 10 and x the radius of the incircle is given by 5/2 = √(((10+x)² – 8²)(8² – (10–x)²)) / (2(8+10+x)). This yields solutions for x around 8.7 and 13.7 — not 6. If you can get accurate figures then you can use Heron's formula for the area of the triangle and subtract the area of the circle.Animated graph: https://www.desmos.com/calculator/gi6e0nnvad

In the 6, 8, 10 right triangle, the diameter extends about one quarter of its length beyond the hypotenuse. Knowing the radius of the circle and the height of the segment inside the triangle, it is possible to determine a good approximation of the area of the segment, which can then be subtracted from the area of the triangle. • RealPro
Lv 7
2 months agoReport

Great answer. "the looks of that picture" will in no way change what's geometrically possible so that may be the worst possible choice for an argument.

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• The area of the green shaded area:

(24 - 19.635) units^2.

= 4.365 units^2

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• Anonymous
2 months ago

its behind the circle

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• 4.37cm2 for the green area, The working out is in the Comment section, a Yahoo glitch makes answers not appear

• Inquizetif
Lv 7
2 months agoReport

The area of the right-angle triangle is (6x8)/2 = 24cm2 ((10 x10) - (8 x 8)) = 36, square root = 6
Area circle (pi x r2) = pi x 2.5 x 2.5 = 19.63cm2
24 - 19.63 = 4.37cm2 for the green area

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