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Can you find area of the Green shaded region? | (Step-by-step explanation) |

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Learn how to find the area of the Green shaded region in the square. Quarter circle and the right triangle. Important Geometry and Algebra skills are also explained: Pythagorean Theorem; area of the square formula; area of a circle formula; area of a triangle formula; Two tangent theorem. Step-by-step tutorial by PreMath.com
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5 сен 2024

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Комментарии : 30

@davoodzamani4254 10 месяцев назад

The Best geometry skills can be learned on your channel. THANK YOU

@PreMath 10 месяцев назад

Glad you think so! ❤️ Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

@quigonkenny 5 месяцев назад

By two tangent theorem, for any two tangents of a circle that converge to the same point, those tangents are the same length. Therefore, PB = AB = 9, and PD = ED = 6, and BD = 9+6 = 15. Triangle ∆DCB: CB² + DC² = BD² (r-9)² + (r-6)² = 15² r² - 18r + 81 + r² - 12r + 36 = 225 2r² - 30r - 108 = 0 r² - 15r - 54 = 0 r² + 3r - 18r - 54 = 0 r(r+3) - 18(r+3) = 0 (r+3)(r-18) = 0 r + 3 = 0 | r - 18 = 0 r = -3 ❌ | r = 18 ✓ r > 0 A = bh/2 = (18-9)(18-6)/2 A = 9(12)/2 = 9(6) = 54 Quarter circle O: A = πr²/4 = π(18²)/4 = 9²π = 81π Green region: A = r² - 81π - 54 A = 18² - 54 - 81π A = 324 - 54 - 81π A = 270 - 81π = 27(10-3π) ≈ 15.53

@misterenter-iz7rz 10 месяцев назад

Using pythagorean theorem, easily we can solve that the radius is 18, and the quarter circle is divided into two sectors, one is 2arctan 1/2, the other is 2arctan 1/3, therefore the green area is 15×18-18^2pi/4=270-81pi=27(10-3pi)=15 53 approximately.😅

@ybodoN 10 месяцев назад

Since OB bisects ∠AOP and OD bisect ∠EOP ⇒ ∠BOD = π / 4. So we can set the equation _arctan (9 / r) + arctan (6 / r) = π / 4._ It will lead to another quadratic equation: r⁴ − 333r² + 2916 = 0. Solutions are r = −18, r = −3, r = 3 and r = 18 (last one accepted).

@jairam4459 9 месяцев назад

Please elaborate two tangents theorem with clarity. Thanks

@loneranger6361 9 месяцев назад

Dear Sir. Thank you so much for your excellent explanation. Thank you you for catering for all students with respect to your excellent manner of teaching

@AmirgabYT2185 5 месяцев назад

S=27(10-3π)≈15,66

@giuseppemalaguti435 10 месяцев назад

(r-9)^2+(r-6)^2=(9+6)^2...r=18...Ag=18^2-(π18^2/4+9*12/2)=270-81π

@JSSTyger 10 месяцев назад

The 2:58 mark gave me the info I needed. :) Area = 270-81π

@prossvay8744 10 месяцев назад

Green area=(18)^2-1/4π(18)^2=1/2(9)(12) =324--81π-54=270-81π

@MegaSuperEnrique 10 месяцев назад

If the blue triangle hadn't been shown, I don't think I would have figured it out

@arnavkange1487 10 месяцев назад

nice sum enjoyed it

@PreMath 10 месяцев назад

Glad you enjoyed Thanks for your feedback! Cheers! 😀

@KAvi_YA666 10 месяцев назад

Thanks for video.Good luck sir!!!!!!!!!!

@PreMath 10 месяцев назад

So nice of you ❤️ Thank you! Cheers! 😀

@marioalb9726 10 месяцев назад

(R-9)²+(R-6)²=(9+6)² (R²-18R+81)+(R²-12R+36)=15² 2R²-30R+117=225 R²-15R-54=0 R = 18 cm A = R.6 + R.9 - ¼π R² A = 15R - ¼πR² A = 15,53 cm² ( Solved √ )