Another Finding Area Problem: trapezoid w/ h=9, median=24

[clb393]

Instructions: Find the area of each figure.
Problem: See attachment for diagram.
[attachment=0:wck66q9y]10-4sg-5.png[/attachment:wck66q9y]

Ok so here another crazy problem, this one is a trapezoid (thanks for correcting me, Subhotosh Khan) with a line cutting through the middle of a trapezoid with 24 m and no measurements of the top or bottom of the trapezoid with a height of 9 m. I would have no clue how to do this. Any help please? :?: (note the red lines are not part of the trapezoid and congruent markings and right angle symbols are in green)

 

[Deleted member 4993]

Re: Another Finding Area Problem

Instructions: Find the area of each figure.
Problem: See attachment for diagram.
[attachment=0:1g4plag3]10-4sg-5.png[/attachment:1g4plag3]

Ok so here another crazy problem, this one is a rhombus - where is it? with a line cutting through the middle of a trapezoid with 24 m and no measurements of the top or bottom of the trapezoid with a height of 9 m. I would have no clue how to do this. Any help please? :?: (note the red lines are not part of the trapezoid and congruent markings and right angle symbols are in green)

What is the equation for the area of a trapezoid?

 

[clb393]

Re: Another Finding Area Problem

Formula for an Area of a Trapezoid: \(\displaystyle A=\frac{1}{2}bh\)

 

[Mrspi]

Re: Another Finding Area Problem

Formula for an Area of a Trapezoid: \(\displaystyle A=\frac{1}{2}bh\)

Actually, the formula for the area of a trapezoid is

A = (1/2)*(b[sub:v4p7fp7i]1[/sub:v4p7fp7i] + b[sub:v4p7fp7i]2[/sub:v4p7fp7i]) * h

where b[sub:v4p7fp7i]1[/sub:v4p7fp7i] and b[sub:v4p7fp7i]2[/sub:v4p7fp7i] are the lengths of the two bases.

BUT....the MEDIAN of a trapezoid is the average of the lengths of the bases, or (1/2)*(b[sub:v4p7fp7i]1[/sub:v4p7fp7i] + b[sub:v4p7fp7i]2[/sub:v4p7fp7i])

So, the area of a trapezoid can also be expressed as A = (median)*height

Now...you have the median for your trapezoid. You also have the height, which is the perpendicular distance between the two bases.

 

[clb393]

Re: Another Finding Area Problem

Ok is it me or am I putting incorrect information down? Ok I'll try that tomorrow. Thanks, Mrspi.

 

[Mrspi]

Re: Another Finding Area Problem

Ok is it me or am I putting incorrect information down? Ok I'll try that tomorrow. Thanks, Mrspi.

The "median" for a trapezoid is the segment joining the midpoints of the two LEGS (the non-parallel sides) of the trapezoid.

Look at the markings on the legs...the two segments on the left side are equal, so the point joining them is the midpoint of that leg. Same on the right side. So, that segment whose length is indicated as 24 IS the median.

 

[clb393]

Thank you, Mrspi! :idea: