# Find the green shaded area?

### 13 Answers

- Anonymous2 months ago
24 - (2.5)^2pimmmmmmm

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- PeriferalistLv 72 months ago
It's right there surrounding the yellow circle.

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- 2 months ago
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.

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- PuzzlingLv 72 months agoReport
They said, "subtract from [the triangle] the area of the circle."

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- JoeLv 62 months ago
It's right there along the inside edges of the triangle.

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- Φ² = Φ+1Lv 72 months ago
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.

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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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- KrishnamurthyLv 72 months ago
The area of the green shaded area:

(24 - 19.635) units^2.

= 4.365 units^2

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- Anonymous2 months ago
its behind the circle

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- InquizetifLv 72 months ago
4.37cm2 for the green area, The working out is in the Comment section, a Yahoo glitch makes answers not appear

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- Log in to reply to the answers