Geometry Shapes & Formulas for Kids - Example & Free Printable PDF

Geometry Formulas for Kids

Geometry is the part of math that helps us measure the world — how far it is around a soccer field, how much paint covers a wall, or how much water fills a fish tank. We answer questions like these using geometry formulas.

This lesson brings together the most important basic geometry formulas in one place, with simple explanations, real examples, and a quick self-check quiz so you can test yourself. You can also download a free printable geometry formulas chart to keep in your notebook.

What You Will Learn (Lesson Objectives)

By the end of this lesson, you will be able to:

• Identify the basic 2D and 3D shapes used in geometry.
• Understand what perimeter, area, volume, and surface area mean.
• Use the correct formula to solve simple geometry problems.
• Explain where these formulas are used in real life.

This lesson supports Grade 3+ math standards (Common Core CCSS.MATH 3.MD — measurement of area and perimeter — and builds toward later volume and surface-area standards).

Key Words to Know

• Perimeter — the distance all the way around a flat shape.
• Area — the amount of flat space inside a 2D shape (square units like cm²).
• Volume — the amount of space inside a 3D (solid) shape (cubic units like cm³).
• Circumference — the distance around a circle.
• Surface area — the total area of all the outside faces of a 3D shape.

Let’s Start Simple — Perimeter

Perimeter is the easiest place to begin because it’s just adding up the sides.

Imagine walking all the way around the edge of a square playground. If one side is 5 meters, and a square has 4 equal sides, you walk 5 + 5 + 5 + 5 = 20 meters. That total distance is the perimeter.

• Square: Perimeter = 4 × s
• Rectangle: Perimeter = 2 × (l + w)
• Triangle: Perimeter = a + b + c (just add the three sides)

Simple example: A rectangle is 6 cm long and 3 cm wide. Perimeter = 2 × (6 + 3) = 2 × 9 = 18 cm.

Next Step — Area of 2D Shapes

Once perimeter makes sense, area is the next step. Area measures the space inside a shape, so it’s always in square units.

• Square: Area = s²
• Rectangle: Area = l × w
• Triangle: Area = ½ × b × h
• Parallelogram: Area = b × h
• Trapezoid: Area = ½ × (b₁ + b₂) × h
• Rhombus: Area = ½ × d₁ × d₂

Simple example: A rectangle 6 cm by 3 cm → Area = 6 × 3 = 18 cm².
Trickier example: A triangle with base 10 cm and height 4 cm → Area = ½ × 10 × 4 = 20 cm². (The ½ is there because a triangle is half of a rectangle.)

Circle Formulas

A circle has no straight sides, so it uses a special number called pi (π), which is about 3.14.

• Diameter: d = 2 × r
• Circumference: C = 2 × π × r (or π × d)
• Area: A = π × r²

(r = radius, the distance from the center to the edge.)

Simple example: A circle has a radius of 5 cm. Circumference = 2 × 3.14 × 5 = 31.4 cm. Area = 3.14 × 5² = 3.14 × 25 = 78.5 cm².

Moving to 3D — Volume

Now we go from flat shapes to solid shapes. Volume measures how much space is inside a solid, so it’s always in cubic units (like cm³).

• Cube: Volume = s³
• Rectangular Prism (box): Volume = l × w × h
• Cylinder: Volume = π × r² × h
• Cone: Volume = ⅓ × π × r² × h
• Sphere (ball): Volume = 4/3 × π × r³
• Pyramid: Volume = ⅓ × base area × h

Simple example: A box 4 cm × 3 cm × 2 cm → Volume = 4 × 3 × 2 = 24 cm³.

Surface Area of 3D Shapes

Surface area is the total area of all the outside faces of a solid — think of how much wrapping paper you’d need to cover a box.

• Cube: SA = 6 × s²
• Rectangular Prism: SA = 2 × (lw + lh + wh)
• Cylinder: SA = 2 × π × r × (r + h)
• Sphere: SA = 4 × π × r²

What Do the Letters Mean?

• s = side  •  l = length  •  w = width  •  h = height
• b = base  •  r = radius  •  d = diameter
• π (pi) = about 3.14
• b₁, b₂ = parallel sides (trapezoid)  •  d₁, d₂ = diagonals

Where We Use Geometry Formulas in Real Life

Geometry isn’t just for school — people use it every day:

• Perimeter: A farmer buying fencing needs the perimeter of the field. You need it to put a border around a poster or garden.
• Area: Buying carpet, tiles, or paint? You need the area of the floor or wall to know how much to buy.
• Volume: Filling a swimming pool, a water tank, or a juice box involves volume.
• Circumference: Bike and car tires, pizza sizes, and running tracks all use circle formulas.

Understanding why a formula matters makes it much easier to remember.

Quick Tips for Success

• Use the same units before calculating (don’t mix cm and m).
• Area → square units (cm², m²). Volume → cubic units (cm³, m³).
• Use π = 3.14 unless told otherwise.
• Draw the shape and label what you know — it helps you pick the right formula.

Try It Out! (Practice Problems)

Work these out on paper, then check the answer key below.

1. Two sides of a triangle are 7 cm and 13 cm. The perimeter is 27 cm. Find the third side.
2. A square has an area of 49 ft². What is the length of one side? What is the perimeter?
3. A rectangle has a width of 4. How long must its length be so the area is 36?
4. One angle of a right triangle is 70°. What are the other two angles?
5. What is the diameter of a circle with an area of 16π?
6. What is the circumference of the circle in problem 5? (Use π = 3.14)

Answer Key (with solutions):

1. 7 cm — 27 − (7 + 13) = 7.
2. Side = 7 ft, Perimeter = 28 ft — √49 = 7, then 4 × 7 = 28.
3. 9 — Area = l × w, so 36 ÷ 4 = 9.
4. 20° and 90° — a right triangle has one 90° angle; 180 − 90 − 70 = 20.
5. 8 — Area = π r², so r² = 16, r = 4, diameter = 2 × 4 = 8.
6. 25.13 — C = π × d = 3.14 × 8 = 25.12 (≈ 25.13).

Get the Free Printable Geometry Formulas Chart

Want every formula on one handy page? Download our free printable geometry formulas chart — great for homework, revision, or pinning above your desk.