MATH SOLVE

2 months ago

Q:
# 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.

Accepted Solution

A:

Answer:"The area of EFGH is always One-half of the area of the rectangle."Step-by-step explanation:Graph is attached.The kite consists of 2 triangle, EFG and EHG.The area of EFG:[tex]\frac{1}{2}*EG*h[/tex]where h is the height from F to EGThe area of EHG:[tex]\frac{1}{2}*EG*h_1[/tex]where [tex]h_1[/tex] is the height from H to EGWe also know that h + h _1 is the width of the rectangle and EG is the length of the rectangleThus,Area of Kite = [tex]\frac{1}{2}*EG*h + \frac{1}{2}*EG*h_1 = RectangleLength*RectangleWidth[/tex]Also, Area of rectangle is rectangle length * rectangle width.Thus, area of kite is always half of that of rectangle, the third choice is right.