Perimeter is the TOTAL DISTANCE around

the outside of a 2D shape

Think of it as the "fence" around the shape

Measured in LINEAR units (cm, m, ft, etc.)

A = l × w

Where:

l = length

w = width (or breadth)

Area is in SQUARE units (cm², m², ft², etc.)

Example: Find the area of a rectangle with length 8 cm and width 5 cm.

A = s²

or A = s × s

Where s = side length

A = b × h

Where:

b = base

h = height (perpendicular to base)

Key Point: The height must be PERPENDICULAR (at 90°) to the base!

A = ½ × b × h

Where:

b = base

h = height (perpendicular to base)

Example: Find the area of a triangle with base 10 cm and height 6 cm.

A = ½ × (b₁ + b₂) × h

Where:

b₁ = first base (top)

b₂ = second base (bottom)

h = height (perpendicular to bases)

Example: Trapezoid with bases 8 cm and 12 cm, height 5 cm.

Circumference is the PERIMETER of a circle

The distance around the circle

C = 2πr

or

C = πd

Where:

r = radius

d = diameter (d = 2r)

π ≈ 3.14 or 22/7

Example: Find the circumference of a circle with radius 7 cm.

A = πr²

Where:

r = radius

π ≈ 3.14 or 22/7

Example: Find the area of a circle with radius 5 cm.

A = (π/4) × d²

Where d = diameter

Area = (πr²)/2

or Area = ½πr²

Perimeter = πr + 2r

(curved part + diameter)

Example: Semicircle with radius 6 cm.

Area = (πr²)/4

or Area = ¼πr²

Perimeter = (πr/2) + 2r

(curved part + two radii)

A compound figure is made up of

TWO or MORE simple shapes combined

Step 1: Break the figure into simple shapes

Step 2: Find the area of EACH simple shape

Step 3: ADD all the areas together

Example: L-shaped figure made of two rectangles.

• Rectangles combined

• Triangles + Rectangles

• Semicircles + Rectangles

• Quarter circles + Squares

• Any combination of basic shapes

Shaded Area = Larger Area − Smaller Area

Common Examples:

• Circle inside a square

• Small circle inside a larger circle (ring/annulus)

• Rectangle with a hole cut out

Example: A square with side 10 cm has a circle with radius 3 cm inside. Find the shaded area.

✓ Perimeter: Distance around (linear units: cm, m, ft)

✓ Area: Space inside (square units: cm², m², ft²)

✓ Height: Must always be perpendicular to base

✓ π value: Use 3.14 or 22/7

✓ Circle formulas: C = 2πr and A = πr²

✓ Semicircle: Half of circle formulas

✓ Quarter circle: One-fourth of circle formulas

✓ Compound figures: Break into simple shapes, add areas

✓ Area between: Larger area − smaller area

✓ Units matter: Always include proper units in answer

Perimeter vs Area:

"Perimeter is a path around the land, Area is the space where you stand!"

Triangle Area:

"Half of base times height - that's the triangle formula done right!"

Circle Circumference:

"Two pi r or pi d - that's the circle's boundary!"

Circle Area:

"Pi r squared is what you need - for circle area guaranteed!"

Trapezoid:

"Add the bases, multiply by height, divide by two - trapezoid area is through!"

Compound Figures:

"Break it up, find each part, add them all - that's how you start!"