Geometry Exam: Shapes and Properties

Shapes and Properties

• A polygon is a 2D shape with at least three sides and three angles.
• Examples of polygons: triangle, quadrilateral
• A hexagon has 6 sides.
• The sum of the interior angles of a triangle is 180 degrees.
• A parallelogram is a quadrilateral with opposite sides of equal length.
• Two types of quadrilaterals:
  • Rectangle: all angles are right angles (90 degrees)
  • Rhombus: all sides are of equal length

Perimeter and Area

• The perimeter of a rectangle is the sum of the lengths of all its sides.
• Formula for perimeter of a rectangle: 2(l + w)
• The area of a square is side length squared.
• Formula for area of a triangle: (base * height) / 2
• The formula is used when the base and height of the triangle are known.
• The circumference of a circle is π times the diameter.
• The area of a circle is π times the radius squared.

Volume

• Volume is the measure of the amount of space inside a 3D shape.
• Formula for volume of a cube: side length cubed
• The volume of a rectangular prism is length times width times height.
• Formula for volume of a cylinder: π times radius squared times height
• The volume of a sphere is (4/3) times π times radius cubed.

Mathematical Drawings

• To draw a square with a diagonal of length 8 cm, use the Pythagorean theorem to find the side length, then construct the square.
• To draw an isosceles triangle, use the given side lengths and angle properties to construct the triangle.