Diagonals of a quadrilateral are equal in length and they are perpendicular. Length of its diagonals is 6 units, consider four statements regarding this quadrilateralI This quadrilateral is a squareII Area of this quadrilateral is 18 square units.III Diagonals bisect each otherIV A diagonal divide the quadrilateral in two triangles of equal area.
Question
Diagonals of a quadrilateral are equal in length and they are perpendicular. Length of its diagonals is 6 units, consider four statements regarding this quadrilateralI This quadrilateral is a squareII Area of this quadrilateral is 18 square units.III Diagonals bisect each otherIV A diagonal divide the quadrilateral in two triangles of equal area.
Solution
I. This statement is true. A quadrilateral with equal and perpendicular diagonals is a square.
II. This statement is also true. The area of a square is calculated by 1/2 * d^2, where d is the length of the diagonal. So, the area of this square is 1/2 * 6^2 = 18 square units.
III. This statement is true as well. In a square, the diagonals bisect each other.
IV. This statement is true. In a square, a diagonal divides the square into two triangles of equal area.
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