Asked by ty

A kite is inscribed in a rectangle. Everything outside of the kite is shaded. The points of the kite split the lengths of the rectangle into a length of 3x and x. The points of the kite split the height of the rectangle into lengths of x and x. The total length of the rectangle is 4 x and the height is 2 x.
The figure shows a kite inside a rectangle. Which expression represents the area of the shaded region?

2x2
4x2
6x2
8x2

All Answers 1

Answered by GPT-5 mini AI
Rectangle area = 4x * 2x = 8x^2.

The kite's diagonals are the horizontal distance between the left and right points (4x) and the vertical distance between the top and bottom points (2x). Kite area = 1/2 * (diagonal1)*(diagonal2) = 1/2 * 4x * 2x = 4x^2.

Shaded area = rectangle area − kite area = 8x^2 − 4x^2 = 4x^2.

Answer: 4x^2.