Calculate area of the Green shaded region | Diagonal of rectangle is 25 | Important skills explained

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Calculate area of the Green shaded region | Diagonal of rectangle is 25 | Important skills explained

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[eckhardfriauf]

Ingenious and tricky.
True to the motto "Think out of the box". And here, the box is a semicircle.

[miguelgnievesl]

I did the following: After finding the value of r, I solved for the area on arc AE and subtracted that value from the area of triangle ABC.

[احمدمحمد-تطج]

تمرين جيد. رسم واضح مرتب. شرح واضح مرتب. شكرا جزيلا لكم والله يحفظكم ويحميكم جميعا. تحياتنا لكم من غزة فلسطين .

[geraldillo]

Interesting solution! I would not never occur to me to do like this, I did it like this; 
green area=upper triangle minus upper left hand corner
=(2r*r)/2 - ((2r)^2-π*r^2)/4

[Abby-hisf]

I love how you use the angle theorem. It simlified a lot

[predator]

Thank you teacher for a very nice problem with an amazing explanation👍🙏.

[fredmertz]

Wow, you have to dust off the thinking cap on this one.. good job !

[kinyutaka]

Okay, I got this one

First, the base of the rectangle is twice the height, because of the semicircle. With a diagonal of 25, that gives us 5x²=625 or x²=125

So, the base is 10√5 and the radius of the circle is 5√5

Bisect the rectangle and the right triangle at the top can slide into the void at the bottom making a clean quarter circle

πr²/4 gives us 31.25π or ≈94.1

[theoyanto]

Another great example, I fell right into the trap, 🤓but thats good learning experience for me 👍🏻

[santiagoarosam]

El rectángulo tiene inscrito un semicírculo de radio “R” → (2R)²+R²=5R²=25² → R²=125 →→ La diagonal corta al radio vertical en su punto medio → La zona verde a la derecha del radio vertical es un triángulo igual al blanco situado a la izquierda del mismo radio → Área verde = (1/4) (Círculo de radio R) =πR²/4 =125π/4 =98.1747
Gracias y saludos cordiales.

[HappyFamilyOnline]

Awesome 👍
Thank you so much for sharing.😊

[vidyadharjoshi]

Green Area = Area of triangle - [1/2*{Area of rectangle - Area of Half Circle}]
= 1/2*Area of Rectangle - [1/2*{Area of Rectangle - Area of Half Circle}] = Area of quarter circle. = 0.25*pi*CDsq
ADsq + CDsq = 625. 5*CDsq = 625. CDsq = 125. Green Area = (125/4)*pi = 98.17

[misterenter-izrz]

25^2=5r^2, so r^2=125, and thus the area Is r^2-(r^2-pi r^2/4)=pi r^2/4=pi 125/4=98.2 approximately. 😃

[spiderjump]

Let the radius of the semicircle be r.

Area of triangle ABC= 1/2x2rxr=r^2
Area of unshaded part of triangle = rxr— 1/4pixr^2
Area of green part=1/4pixr^2
By Pythagorean theorem, 5r^2= 25x25
r^2=125

Hence area of shaded
=125pi/4

[Juliana-kyzr]

Thank you Sir. Please, help me. Why can't I consider the CÂD angle 45 degrees? Ex: if I consider the diagonal cutting 45 degrees, by the trigonometric ratio of sine, R becomes 25/2root2.

[marioalb]

Siendo un rectángulo de relación 2 a 1, el ángulo del segmento diagonal d ó AC respecto a la vertical, es:
α=atan (2/1)= 63, 435°
Luego, el radio del círculo es:
R= d cos α
R= 25 cos 63.435°
R= 11, 18 cm

El área sombreada verde es equivalente al área de un cuarto de circulo:
Área= πR²/4
Área= π.11, 18²/4
Área= 98, 17 cm² ( Solved √ )

[parthtomar]

Sir please upload a video for the explanation of matrices from basic for class11 please sir upload as fast as you can

[carstenlarsen]

nice trick to turn the triangel and outcome 1/4 of the citkel-
i did the the numbers all in head- thats more fun..

[EnnioPiovesan]

Considering the right triangle ABC we can write AB²+BC²=AC² --> r²+4r²=25² --> 5r²=5²·5² --> r=5√5.
The area Ae between AB, BE and arc AE is half the difference between the area of the rectangle and the semicircle: Ae = (1/2) [r·2r - (1/2)πr²]=(1/2)[2r² - (1/2)πr²]=(1/4)r²(4-π)
=(125/4)(4-π).
The green area Ga is the difference between the area of the triangle ABC and the above area Ae. So the green area is:
Ga=(1/2)(r·2r) -

[Gbahati]

I need at least two questions which explain how to calculate the angle in triangular prism