Lección 10
Bases y alturas de triángulos
Usemos diferentes parejas de bases y alturas para encontrar el área de un triángulo.
Problema 1
En cada triángulo, una base se etiqueta \(b\). Dibuja un segmento de recta que muestre su altura correspondiente. Usa una tarjeta bibliográfica para ayudarte a dibujar una línea recta.
![3 triangles with 1 side on each labeled b.](https://cms-im.s3.amazonaws.com/e7XsZDTn9zvbgdYwBN6WFXx5?response-content-disposition=inline%3B%20filename%3D%226-6.1.C.PP_Image_27.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.C.PP_Image_27.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000033Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a7b6a3319a875566506f0974ec699a9037cb0194b1ce4523c31472eb08d86c36)
Problema 2
Selecciona todos los triángulos que tienen un área de 8 unidades cuadradas. Explica cómo lo sabes.
![5 triangles on grid labeled A, B, C, D, E.](https://cms-im.s3.amazonaws.com/XZJAmPFrvQ59CDRFsg1U4Xfx?response-content-disposition=inline%3B%20filename%3D%226-6.1.C.PP_Image_29.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.C.PP_Image_29.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000033Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=89492ce59c1dc141fc48b246c72967744d833b8f7ec9bb55fd04f0441f14b977)
Problema 3
Encuentra el área del triángulo. Muestra tu razonamiento.
![Triangle on grid, base = 6, height = 4](https://cms-im.s3.amazonaws.com/UUQo1fWRMutt4tJgvKxPbUbr?response-content-disposition=inline%3B%20filename%3D%226-6.1.C.PP_Image_30.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.C.PP_Image_30.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000033Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fbd033f072f43514c2cec211065d0a4993b7d1225013fc6e8c120bb22f95c919)
Si tienes dificultades, considera cuidadosamente cuál lado del triángulo usar como la base.
Problema 4
¿El lado \(d\) puede ser la base de este triángulo? Si sí, ¿cuál distancia sería la altura correspondiente? Si no, explica por qué no.
![A triangle with sides labeled d, e, and f. The angle opposite side D is a right angle. A segment labeled g is perpendicular to side d and extends to the opposite vertex.](https://cms-im.s3.amazonaws.com/prUqTf2JuReKCiXBRShyzV6e?response-content-disposition=inline%3B%20filename%3D%226-6.1.C.PP.New.Image.10.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.C.PP.New.Image.10.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000033Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a88a0e242349c8dd93c8453d0bd00ff4c79cc0671c8a1cf75f07e8f970877113)
Problema 5
Encuentra el área de esta figura. Muestra tu razonamiento.
![A shape with six sides. There are two vertical sides measuring five units, two angled sides that fall 2 units over 4 units and two sides that fall 2 units over 2 units.](https://cms-im.s3.amazonaws.com/2YXc9UpF9MyRVaLHULxCRLAZ?response-content-disposition=inline%3B%20filename%3D%226-6.1.A.PP.New.Image.18a.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.A.PP.New.Image.18a.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000033Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=40ada8a26a317ccdda7be0f1ebd61330f9501895fa093c581d7d1982d8da0beb)
Problema 6
Esboza en la cuadrícula dos paralelogramos diferentes que tengan la misma área. Etiqueta una base y una altura de cada uno y explica cómo sabes que las áreas son iguales.
![Image of a grid.](https://cms-im.s3.amazonaws.com/vupNoA5g96AkAtsSrCipKyG6?response-content-disposition=inline%3B%20filename%3D%226-6.1.A3.Image.00.Blank-Grid.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.A3.Image.00.Blank-Grid.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000033Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=104263217c60e9ae1ceb23771b6c3a75a92b43c1f0094aa3f9c81680b7f0f480)