UNIDAD III 

RESOLUCION DE TRIANGULOS RECTANGULOS

APLICACIÓN DE LA TRIGONOMETRIA

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UNIDAD II

14.04.2013 20:55

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 2π 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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