Properties of Shapes：練習題

Which of the following statements about a rhombus is not always true?

A quadrilateral has exactly one pair of parallel sides. Two of its interior angles are right angles. What is the most specific name for this shape?

A shape is made by attaching a square with side length \(6\) cm to one of the longer sides of a rectangle that measures \(10\) cm by \(6\) cm. What is the total perimeter of the new combined shape if the shared side is hidden inside the shape?

Which of the following 3D shapes has exactly 4 faces, 4 vertices, and 6 edges?

Which property is shared by both a rectangle and a parallelogram?

Identify the 3D shape that has 6 identical square faces, 12 edges, and 8 vertices.

A quadrilateral has two pairs of equal adjacent sides, but opposite sides are not equal. One of its diagonals is a line of symmetry and bisects the other diagonal at a right angle. What is the name of this shape, and how many pairs of equal opposite angles does it have?

Identify the 3D shape that has 2 circular bases and 1 curved surface. How many edges does this shape have?

Consider a 3D shape with 8 vertices, 12 edges, and 6 faces. All its faces are identical squares.
(a) What is the name of this 3D shape?
(b) If each edge of this shape is \( 5\text{ cm} \) long, what is the total length of all its edges?
(c) What is the total surface area of this shape?

Identify the properties of the following 2D shapes:
(a) A shape has 4 sides of equal length and no right angles. What is the specific name of this quadrilateral?
(b) How many lines of symmetry does a regular hexagon have?
(c) If a triangle has one angle of \(90^{\circ}\) and two sides of equal length, what are the sizes of the other two angles?