Answer:
96 cm²
Step-by-step explanation:
You want to know the combined areas of triangles AED and BEC in parallelogram ABCD with AE⊥CD.
Area formulas
The area of the parallelogram is given by the formula ...
A = bh
where b is the length of one side, and h is the perpendicular distance to the other side.
For this parallelogram, b=16 cm and h=12 cm, so the area is ...
A = (16 cm)(12 cm) = 192 cm² . . . . . parallelogram area
The area of triangle AEB has the formula ...
A = 1/2bh
where b is the base, and h is the perpendicular distance to the opposite vertex.
For triangle AEB, the lengths b and h are the same as for the parallelogram, so the triangle area is ...
A = 1/2(16 cm)(12 cm) = 96 cm²
Area of interest
The total area of ∆AED and ∆BEC is the difference between the parallelogram area and the area of ∆AEB:
192 cm² -96 cm² = 96 cm²
The areas of ∆AED and ∆BED total 96 cm².
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Additional comment
Angles DEA and BAE are "alternate interior angles" where transversal AE crosses parallel lines AB and CD. As such, they are congruent. Angle DEA is marked as a right angle, so angle BAE is also a right angle.
As you can see, any triangle that has a base that is one side of a parallelogram and a vertex on the other side will have an area that is half the area of the parallelogram.
