Kite efgh is inscribed in a rectangle such that f and h are midpoints and eg is parallel to the side of the rectangle.
which statements describes how the location of segment eg affects the area of efgh?
a.) the area of efgh is 1/4 of the area of the rectangle if e and g are not midpoints
b.) the area of efgh is 1/2 of the area of the rectangle only if e and g are midpoints
c.) the area of efgh is always 1/2 of the area of the rectangle.
d.) the area of efgh is always 1/4 of the area of the rectangle.

C

Step-by-step explanation:

EFGH is a kite, so EF ≅ FG and EH ≅ HG.

The area of the kite consists of two area of triangles EFG and EHG.

1. Area of triangle EFG:

where h is the height drawn from point F to the side EG.

1. Area of triangle EHG:

where H is the height drawn from point H to the side EG.

3. Note that

So,

Thus, option C is true (the area of the kite doesn't depend on ratio in which points E and G divide the side)

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step-by-step explanation:

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