Shapes, properties, perimeter, area basics
Elementary Foundations • K-5
Geometry is the study of shapes and space. Look around you right now -- you will see rectangles (doors, windows, books), circles (clocks, plates), and triangles (roof shapes, pizza slices). Understanding shapes helps us describe and build the world around us.
Flat shapes are called two-dimensional (2D) shapes because they have length and width but no thickness. Here are the shapes you need to know:
| Shape | Sides | Corners (Vertices) | Special Properties |
|---|---|---|---|
| Triangle | 3 | 3 | Sides can be all equal, two equal, or all different |
| Square | 4 | 4 | All sides equal, all corners are right angles |
| Rectangle | 4 | 4 | Opposite sides equal, all corners are right angles |
| Circle | 0 | 0 | Perfectly round, every point is the same distance from the center |
| Pentagon | 5 | 5 | Five straight sides |
| Hexagon | 6 | 6 | Six straight sides |
Every square is also a rectangle (it has 4 sides and 4 right angles). But not every rectangle is a square -- a rectangle only becomes a square when all four sides are the same length.
The perimeter is the total distance around a shape. To find it, add up the lengths of all the sides.
A rectangle has a length of 8 cm and a width of 3 cm.
A rectangle has two long sides and two short sides:
Shortcut: Perimeter = 2 x (length + width) = 2 x (8 + 3) = 2 x 11 = 22 cm.
A triangle has sides of 5 in, 7 in, and 4 in.
The area is the amount of space inside a flat shape. We measure area in square units (like square centimeters, written cm²).
A rectangle is 5 units long and 3 units wide. Imagine filling it with unit squares:
Count the squares: 15. Or use the formula:
Perimeter and area are different! Perimeter is the distance around a shape (measured in cm, in, ft). Area is the space inside a shape (measured in cm², in², ft²). Think of perimeter as the fence around a yard, and area as the grass inside it.
1. How many sides does a hexagon have?
A hexagon has 6 sides.
2. Find the perimeter of a square with sides of 6 cm.
A square has 4 equal sides: Perimeter = 6 + 6 + 6 + 6 = 4 x 6 = 24 cm.
3. Find the area of a rectangle that is 9 ft long and 4 ft wide.
Area = length x width = 9 x 4 = 36 square feet (36 ft²).
4. A garden is shaped like a rectangle, 10 m long and 6 m wide. How much fencing is needed to go around it?
Perimeter = 2 x (10 + 6) = 2 x 16 = 32 meters of fencing.
5. True or false: A square with sides of 5 cm has the same perimeter as a rectangle that is 6 cm by 4 cm.
True. The square's perimeter = 4 x 5 = 20 cm. The rectangle's perimeter = 2 x (6 + 4) = 2 x 10 = 20 cm. They are the same!
Summary: 2D shapes are defined by their sides and corners. Perimeter is the distance around a shape (add all the sides). Area is the space inside (for rectangles, multiply length by width). Always include the correct units: regular units for perimeter, square units for area.