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 EG
The area of EHG:
[tex]\frac{1}{2}*EG*h_1[/tex]
where [tex]h_1[/tex] is the height from H to EG
We also know that h + h _1 is the width of the rectangle and EG is the length of the rectangle
Thus,
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.
The area of EFGH is always One-half of the area of the rectangle.
We have given that the kite EFGH is inscribed in a triangle and F and H are midpoints and EG is parallel to the side of rectangle.
The kite consists of 2 triangle that are EFG and EHG.
[tex]\frac{1}{2}\times height\times base[/tex]
Therefore, by using the formula we can find the area of the triangle
In a triangle EFG
[tex]=1/2 \times EG\times h[/tex]......(1)where h is the height from F to
where h is the height from F to EG
Also the area of EHG:
[tex]A(\Delta EHG)=\frac{1}{2} EG\times h_1[/tex]
where is the height from H to EG
We also know that [tex]h + h _1[/tex] is the width of the rectangle and EG is the length of the rectangles.
Area of Kite = [tex]Area of the rectangle=\frac{1}{2} \times EG\times h+\frac{1}{2} \times EG\times h_1[/tex]
Also, The area of a rectangle is rectangle length × rectangle width.
Thus, The Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle.
The statement describes how the location of segment EG affects the area of EFGH is the area of EFGH is always One-half of the area of the rectangle.
To learn more about the rectangular kite visit:
https://brainly.com/question/2292872
