Answer:
The area of the parallelogram is 65 square units
Explanation:
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One way to find the area of a parallelogram is by using decomposition, which involves dividing the parallelogram into two triangles and then finding the area of each triangle. To do this, you can use the formula for the area of a triangle:
Area of a triangle = (base × height) / 2
where the base is one of the sides of the triangle and the height is the length of the perpendicular line segment from the base to the opposite vertex.
To apply this formula to a parallelogram, you can choose one of the sides as the base and the length of the perpendicular line segment from the opposite vertex to the base as the height. Then, you can calculate the area of each triangle and add them together to get the area of the parallelogram.
In your case, assuming that the base of the parallelogram is x units and the height is h units, we can divide the parallelogram into two triangles as shown:
/ |\
/ | \
/ | \
/ |h \
/ | \
/ | \
/______|______\
x y
Sorry for the bad art.
Triangle 1: base = x, height = h, area = (x × h) / 2
Triangle 2: base = y, height = h, area = (y × h) / 2
Therefore, the total area of the parallelogram is:
Area of parallelogram = Area of triangle 1 + Area of triangle 2
= (x × h) / 2 + (y × h) / 2
= (x + y) × h / 2
= (8 + 2) × 13 / 2
= 65 square units
So the area of the parallelogram is 65 square units.