Volume of Triangle w/ xy-plane Vertices - Help Needed

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In summary, the conversation is about finding the volume of a solid with a triangular base in the xy-plane. The cross sections of the solid are equilateral triangles perpendicular to the y-axis. The conversation also includes a discussion about the height of the triangles, with suggestions of using similar triangles.
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gillyr2
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Question: Find the volume of the solid whose base is the triangular region of the xy-plane with vertices (0,0),(1,0),(0,1) and whose cross sections perpendicular to the y-axis are equilateral triangles.

I have the problem set up. just don't know how to get the cross sections of the triangles. i know the area is 1/2 bh i thought maybe similar triangles where the height would be sqrt(3)/4x and x=1-y. am i close? help
 
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gillyr2 said:
i know the area is 1/2 bh i thought maybe similar triangles where the height would be sqrt(3)/4x and x=1-y. am i close? help

Hi gillyr2! :smile:

yeah … close … :wink:

though I don't understand what you mean by "similar triangles" …

these are equilateral (3 x 60º) triangles of side (as you say) 1 - x …

so h = … ? :smile:
 

FAQ: Volume of Triangle w/ xy-plane Vertices - Help Needed

What is the formula for finding the volume of a triangle in the xy-plane?

The formula for finding the volume of a triangle in the xy-plane is V = (1/2) * b * h * d, where b is the length of the base, h is the height of the triangle, and d is the distance from the xy-plane to the third vertex.

How do you determine the height of a triangle in the xy-plane?

The height of a triangle in the xy-plane can be determined by finding the distance between the base and the third vertex, using the distance formula d = √(x2-x1)^2 + (y2-y1)^2.

Is there a specific unit for measuring the volume of a triangle in the xy-plane?

Yes, the unit for measuring the volume of a triangle in the xy-plane is cubic units, as the volume is a three-dimensional measurement.

Can the volume of a triangle in the xy-plane be negative?

No, the volume of a triangle in the xy-plane cannot be negative as it represents the amount of space enclosed by the triangle, which is always a positive value.

How does changing the third vertex of a triangle in the xy-plane affect its volume?

Changing the third vertex of a triangle in the xy-plane can significantly affect its volume. If the third vertex is moved closer to the xy-plane, the volume will decrease, and if it is moved further away, the volume will increase.

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