UNIDAD III 

RESOLUCION DE TRIANGULOS RECTANGULOS

APLICACIÓN DE LA TRIGONOMETRIA

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UNIDAD II

AREAS  Y PERIMETROS 

Área del triángulo

dibujo

fórmulas

Hallar el área y el perímetro del siguiente triángulo:

dibujo

P = 2 · 11 + 7.5 = 29.5 cm

fórmulas

 

Cuadrado

dibujo

fórmulas

fórmulas

Ejemplo

Calcular el área y el perímetro de un cuadrado de 5 cm de lado.

cuadrado

A = 52 = 25 cm2

Rectángulo

dibujo

fórmulas

fórmulas

Ejemplo

Calcular el área y el perímetro de un rectángulo de 10 cm de base y 6 cm de altura.

rectángulo

P = 2 · (10 + 6) = 32 cm

A = 10 · 6 = 60 cm2

Rombo

dibujo

fórmulas

fórmulas

Ejemplo

Calcular el área y el perímetro de un rombo cuyas diagonales miden 30 y 16 cm, y su lado mide 17 cm.

dibujo

P = 4 · 17 = 68 cm

fórmulas

Área del romboide

dibujo

P = 2 · (a + b)

A = b · h

Ejemplo

Calcular el área y el perímetro de un romboide de 4 y 4.5 cm de lados y 4 cm de altura.

dibujo

P = 2 · (4.5 + 4) = 17 cm

A = 4 · 4 = 16 cm2

Área del trapecio

dibujo

fórmulas

Ejemplo

Calcular el área y el perímetro del siguiente trapecio:

dibujo

fórmulas

Área de un polígono regular

dibujo

fórmulas

n es el número de lados

fórmulas

Ejemplos

Calcular el área y el perímetro de un pentágono regular de 6 cm de lado.

pentágono regular

solución

solución

P = 5 · 6 = 30 cm

solución

Calcular el área y el perímetro de un hexágono regular inscrito en una circunferencia de 4 cm de radio.

dibujo

solución

solución

P = 6 · 4 = 24 cm

 

Perímetro de un círculo

Una circunferencia es el perímetro de un círculo.

radio y diametro de la circunferencia

La longitud de una circunferencia es igual a por el radio.

fórmula

La longitud de una circunferencia es igual a π por el diámetro.

longitud de una circunferencia


 

Ejercicio

Calcular la longitud de una rueda de 90 cm de diámetro.

dibujo

1º A partir del diámetro

fórmula

2º A partir del radio

fórmula

fórmula

AREAS  Y VOLUMNENES   DE LOS CUERPOS SOLIDOS

 

 

Calcula el área lateral, total y el volumen de una pirámide cuadrangular de 10 cm de arista básica y 12 cm de altura.

pirámide cuadrangularapotema lateral de la pirámide

apotema lateral de la pirámide

perímetro

área lateral de la pirámide

área de la pirámide

volumen de la pirámide

Calcula la cantidad de hojalata que se necesitará para hacer 10 botes de forma cilíndrica de 10 cm de diámetro y 20 cm de altura.

dibujo


 

solución

solución


Calcular el área del círculo resultante de cortar una esfera de 35 cm de radio mediante un plano cuya distancia al centro de la esfera es de 21 cm.

radio de una esfera


radio de una esfera

radio de una esfera

 

Calcular el área del círculo resultante de cortar una esfera de 35 cm de radio mediante un plano cuya distancia al centro de la esfera es de 21 cm.

radio de una esfera


radio de una esfera

radio de una esfera

Calcula el volumen, en centímetros cúbicos, de una habitación que tiene 5 m de largo, 40 dm de ancho y 2500 mm de alto.

dibujo


 

solución

solución

solución

solución

 

 

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COMENTARIOS FINALES

MY STORY

This is a story based off of one of my friends and I. He is my best friend in the entire world. I wouldnt trade what we have for anything.
Adam is my best friend. He is about 63 and is kind of tan considering its always cold here. Hes skinny but has a lot of muscle. He is the star player on our schools basketball and baseball teams. He is so super nice to everyone and is very smart. Hes in a lot of my classes. Hes kind of shy and quiet too.
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Caravan of love

God I need a cigarette! I gasped as I collapsed, exhausted, at the top of the small mountain my team had just hiked up in the Lake District.
Youre supposed to be setting us a good example. Khalid laughed as he flopped down next to me quickly followed by his two schoolmates.
Fu…To Hell with that! I laughed, I deserve one after a walk like that.
Still laughing at me puffing and panting the boys whispered something, then Khalid turned to me and asked nervously; Do you really want a smoke?
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Turning His Angel Into A Slut

I tried so hard to remember what had gotten me here.Could it have happened that first night in the movie theatre?Could it have been when he was fucking me?Could it have been in the theatre today?These are all questions that went through my head.
The first night we went to the movies turned out to be a most memorable one.My Daddy wanted a blow job.He didnt care who was around, or if they saw, he only wanted to release and release he did.He unzipped his pants and pulled them down away from his cock then took his hand and wrapped it around the back of my neck.
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Bright and Early

Anya lay on her bed, staring at the ceiling of her moderately-sized dorm room. Her digital alarm clocks LCD display burned a crisp 4:05 AM in the darkness. In two hours and a half she would have to go to class. Her music player was still operating, singing out Pink Floyds later, more ambient sounds. In her head, she went over all the homework she had and every project due withing the next three weeks. Everything was according to schedule. She continued to stare, thinking about how she would make the most of the first weekend her roommate, Tara, was gone.
https://www.tumblr.com/blog/view/arthur324017668

First gay experience

My dad and I had always been close in what some people would call an odd way. My mom passed away when I was 3 so dad basically raised me by himself. Growing up we did everything together. Cuddled (sometimes he would be naked) and watched sports, went to games, he would give me baths, and some other stuff. But as I got older I noticed how dad would start to look at me more and more and for longer amounts of time.
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Sexy story

Its hard to pinpoint exactly when it dawned upon me for the first time, but I think it was as I was relaxing in the hot tub room with Melia after I had fucked her for the first time. The realization hit me; I was essentially a god here in this primitive age of 2015. And, if I were to confine my time travels to the past from 2015, nothing could stop me from doing as I wanted. I had three beautiful women with me on board my all powerful craft, time was on my side- the technology given to me by the Jogany meant that I would not age for a couple of thousand years.
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Homework


Together with about three subscores, which usually means every single grader may offer you everywhere in the"3" into some"1 2" in exactly the maximal. The two graders can provide you that their particular collection of subscores, which sets your last score in among a"6" in the best bottom, and also a"2 4" to get a fantastic SAT Essay.
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