Quadrilaterals (rectangle, square, trapezium, rhombus, parallelogram)：練習問題

Which of the following quadrilaterals must have four equal sides but does not necessarily have four right angles?

In a quadrilateral \(PQRS\), the sides \(PQ\) and \(RS\) are parallel. The lengths of the other two sides \(QR\) and \(SP\) are equal, but they are not parallel to each other. What is the most specific name for this quadrilateral?

In a quadrilateral \(ABCD\), \(\angle A = 2x\), \(\angle B = 3x\), \(\angle C = 4x\), and \(\angle D = 90^{\circ}\). Find the value of the largest angle in the quadrilateral.

Which of the following quadrilaterals has two pairs of parallel sides and four right angles, but its four sides are not necessarily equal in length?

In the figure, \(ABCD\) is a parallelogram. The area of triangle \(ABC\) is \(48\text{ cm}^2\). If the height of the parallelogram with respect to base \(BC\) is \(8\text{ cm}\), find the length of side \(BC\).

Which quadrilateral has exactly one pair of parallel sides?

In the figure, the area of a parallelogram with a base of \( 12 \) cm and a height of \( 8 \) cm is equal to the area of a trapezium. If the upper base of the trapezium is \( 7 \) cm and the lower base is \( 9 \) cm, find the height of the trapezium in cm.

In the figure, \(ABCD\) is a rhombus with a perimeter of \(52\text{ cm}\) and the length of diagonal \(AC\) is \(10\text{ cm}\). If the area of triangle \(ABC\) is \(60\text{ cm}^2\), find the height of the rhombus when side \(BC\) is taken as the base.

A rectangular garden has a length of \(12\text{ m}\) and a width of \(8\text{ m}\).
(a) Find the perimeter of the garden.
(b) If a square pond with a side length of \(3\text{ m}\) is built inside the garden, what is the remaining area of the garden?

In a quadrilateral \(ABCD\), \(AB\) is parallel to \(DC\), and \(AD\) is parallel to \(BC\). The length of \(AB\) is \((3x + 2)\text{ cm}\) and the length of \(DC\) is \(14\text{ cm}\). The height of the shape is \(8\text{ cm}\).
(a) Identify the type of quadrilateral.
(b) Solve for \(x\).
(c) If this shape is transformed into a rhombus with the same perimeter, and the side of the rhombus is \(12\text{ cm}\), find the length of side \(AD\) in the original shape.