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 midpointsB.) The area of EFGH is 1/2 of the area of the rectangle only if E and G are midpointsC.) 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.

Answer:CStep-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:[tex]A_{\trangle EFG}=\dfrac{1}{2}\cdot EG\cdot h,[/tex]where h is the height drawn from point F to the side EG.1. Area of triangle EHG:[tex]A_{\trangle EHG}=\dfrac{1}{2}\cdot EG\cdot H,[/tex]where H is the height drawn from point H to the side EG.3. Note that [tex]EG \cong \text{rectangle's length}[/tex][tex]h+H\cong \text{rectangle's width}[/tex]So,[tex]A_{\text{kite }EFGH}\\ \\=A_{\triangle EFG}+A_{\triangle EHG}\\ \\=\dfrac{1}{2}\cdot EG\cdot (h+H)\\ \\=\dfrac{1}{2}\cdot \text{rectangle's length}\cdot \text{rectangle's width}\\ \\=\dfrac{1}{2}A_{\text{rectangle}}[/tex]Thus, option C is true (the area of the kite doesn't depend on ratio in which points E and G divide the side)