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

Answer:

The area of EFGH is always One-half of the area of the rectangle.

Step-by-step explanation:

If F and H are midpoints of sides of rectangle then FH is parallel to the other side of rectangle so FH is perpendicular to the EG. That means the lenght of FH is equal to lenght of rectangle, and the lenght of EG is equal to width of rectangle.

So the area of the rectangle:  $A_{rectangle}=EG\cdot FH$

FH ⊥ EG so the area of quadrangle EFGH:

$A_{_{EFGH}}=\frac12EG\cdot FH=\frac12A_{rectangle}$

no matter the location of segment EG

Answer 2

Answer:

C

Step-by-step explanation: