Question

Kite E F G H is inscribed within a rectangle. Points F and H are midpoints of the sides of the rectangle. Points E and G are parallel to the side of the rectangle.
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 statement describes how the location of segment EG affects the area of EFGH?

The area of EFGH is One-fourth of the area of the rectangle if E and G are not midpoints.
The area of EFGH is One-half of the area of the rectangle only if E and G are midpoints.
The area of EFGH is always One-half of the area of the rectangle.
The area of EFGH is always One-fourth of the area of the rectangle.

Answer 1

The area is always one-half of the area of the rectangle.

Reason: Let the rectangle have width w and height h. Since F and H are midpoints of opposite vertical sides, FH is a horizontal segment of length w. EG is a vertical segment joining the top and bottom sides, so EG = h and EG ⟂ FH. For a kite the area = 1/2 × (product of the diagonals) = 1/2 · w · h, which is half the rectangle's area. E and G need not be midpoints for this to hold.