Area of a trapezoid in triangle.

[zinke]

HI I am trying to understand how to solve this problem. Area of a trapezoid inside of a triangle.

 

[Dr.Peterson]

I would start with similar triangles to find the length of the midline. That will also let you find other quantities you may want to know).

There are several ways to go from there; please show us your thoughts, and we can help you bring them to reality.

 

[MarkFL]

Hello, and welcome to FMH!

I think what I would do here is observe that the small unshaded triangular portion of the large triangle is similar to the large triangle. Based on that, can you find the length of the boundary dividing the shaded trapezoid from the unshaded triangle within the large triangle?

Can you see that the horizontal altitudes of the two figures within the large triangle must be the same?

These two concepts will give you all you need to compute the area of the trapezoid. What do you get?

 

[pka]

I am trying to understand how to solve this problem. Area of a trapezoid inside of a triangle.

Do you know the area of a trapezoid? Look here
Now what Prof. Peterson calls "midline" is the upper base equal in length to half the other base. the midline also determines the height.
Now post your work.

 

[MarkFL]

Another approach would be to observe that the area of the trapezoid is 3/4 the area of the large triangle.

 

[zinke]

Greetings and thank you for the welcome.
Area of trapezoid ~ A=a+b/2*h, so if a midline is equal in length to half the other base 24 cm and height should be 9, the half of 18 cm.
12+24/2*9=18*9=162 cm² which is 3/4 of the area of a big triangle 216 cm². I never realized that "midline" is actually half a length of the big base. Still confuses me a bit but all your replies helped me solve this. Thank You

 

[Dr.Peterson]

For more on midlines (or midsegments), see https://mathbitsnotebook.com/Geometry/SegmentsAnglesTriangles/SATMidSegments.html.

The same similar triangles that prove that theorem are useful for a lot of other things, so they're worth being aware of. (I deliberately used the term so you might search for it and learn about the theorem, though it wasn't essential.

 

[zinke]

For more on midlines (or midsegments), see https://mathbitsnotebook.com/Geometry/SegmentsAnglesTriangles/SATMidSegments.html.

The same similar triangles that prove that theorem are useful for a lot of other things, so they're worth being aware of. (I deliberately used the term so you might search for it and learn about the theorem, though it wasn't essential.

Thank You, this page will help.