Question

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 midpoints

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

C.) 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 1

C.) The area of EFGH is always 1/2 of the area of the rectangle.

Explanation:

Answer 2

C

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:

`A_(\trangle EFG)=(1)/(2)\cdot EG\cdot h,`

where h is the height drawn from point F to the side EG.

1. Area of triangle EHG:

`A_(\trangle EHG)=(1)/(2)\cdot EG\cdot H,`

where H is the height drawn from point H to the side EG.

3. Note that

`EG \cong \text{rectangle's length}`

`h+H\cong \text{rectangle's width}`

So,

`A_{\text{kite }EFGH}\\ \\=A_(\triangle EFG)+A_(\triangle EHG)\\ \\=(1)/(2)\cdot EG\cdot (h+H)\\ \\=(1)/(2)\cdot \text{rectangle's length}\cdot \text{rectangle's width}\\ \\=(1)/(2)A_{\text{rectangle}}`

Thus, option C is true (the area of the kite doesn't depend on ratio in which points E and G divide the side)