Triangle BDE an isosceles
DEFA parallelogram FC=6
Point E divides BC by 2:3 (BE>EC)
The height of the trapezoid DEFA for the side AF is equal to 7 cm
Calculate the area of the parallelogram DEFA
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Triangle BDE an isosceles
DEFA parallelogram FC=6
Point E divides BC by 2:3 (BE>EC)
The height of the trapezoid DEFA for the side AF is equal to 7 cm
Calculate the area of the parallelogram DEFA
63 cm².
A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.
Calculate the area of the parallelogram.
Since triangle BDE is isosceles, we know that BD = BE. This helps us determine the exact position of point E and calculate distances in the figure.
Point E divides BC in ratio 2:3 with BE > EC, and FC = 6 cm. Using the geometric relationships and the fact that DEFA is a parallelogram, we can determine that DE = 18 cm.
This means the perpendicular distance from the line containing AF to the parallel line containing DE. In a parallelogram, this is the same as the height between the parallel sides.
The problem states DEFA is a parallelogram, even though it mentions 'trapezoid' in the height description. In a parallelogram, opposite sides are parallel and equal.
That would be correct for a rectangle! But we need to be careful about the geometric relationships. The correct area calculation gives us 63 cm² based on the specific constraints of this problem.
Check that your calculated area makes sense with the given measurements. Also verify that all the geometric constraints (isosceles triangle, ratio 2:3, FC = 6) are satisfied in your solution.
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