Pythagorean Theorem Worksheet (Free Printable + Practice Problems)

The Pythgorean Theorem is one of the most important topics in geometry, and it forms the base of the trigonometry, and even engineering and real-world measurements. It's also important for exams. If you'rre a student, teacher or parent, this Pythagorean Theorem Worksheet will help you understand, apply and practice it easily and it will make sure you fully understand the concept.

What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right-angled triangle,

the square of the hypotenuse is equal to the sum of the squares of the other two sides.

That is,

$$a^2 + b^2 = c^2$$

Where:

• a = one side
• b = other side
• c = hypotenuse (longest side)

Example: If one side is 3 cm and the other is 4 cm,

$$c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = 5$$

So, the hypotenuse is 5 cm.

Why is the Pythagorean Theorem Important?

• ✅ Helps calculate distances between two points
• ✅ Used in construction, navigation, and physics
• ✅ Foundation for trigonometry and coordinate geometry
• ✅ Builds strong problem-solving skills

Free Pythagorean Theorem Worksheet PDF (Download)

👉 [Download Pythagorean Theorem Worksheet PDF – Free Printable] (You can create this as a downloadable PDF on your site or Study Friend app.)

Worksheet Contents:

1. Formula recap
2. Easy-level problems
3. Moderate-level practice
4. Real-world applications
5. Challenge questions with answers

Pythagorean Theorem Practice Problems (With Answers)

Set 1 – Basic Problems

1. If a = 3 cm and b = 4 cm, find c. → Answer: 5 cm
2. a = 5 m, b = 12 m → c = ? → Answer: 13 m
3. a = 7 cm, c = 25 cm → b = ? → Answer: 24 cm

Set 2 – Real-Life Word Problems

1. A ladder 10 m long leans against a wall. The base is 6 m from the wall. How high does the ladder reach? → Answer: 8 m

2. A TV is 32 inches diagonally. If the width is 28 inches, find the height. → Answer: √(32² − 28²) = 16.97 ≈ 17 inches

Set 3 – Find Missing Side (Mixed Practice)

a (cm)	b (cm)	c (cm)	Missing Side	Answer
6	8	?	Hypotenuse	10
?	9	15	One leg	12
5	?	13	One leg	12
9	12	?	Hypotenuse	15

How to Use This Worksheet

• Students: Practice 15 mins a day to strengthen geometry basics.
• Teachers: Use it as classwork or homework.
• Parents: Print and guide your child through examples.

Bonus: Fun Facts About the Pythagorean Theorem

• Named after Pythagoras, a Greek mathematician.
• Works only for right-angled triangles.
• Used in GPS systems, surveying, and even computer graphics.

Final Tip

Practice is the key to mastering geometry. Download the free worksheet, solve one set daily, and soon the Pythagorean theorem will feel like second nature!

💬 Did you find this worksheet helpful? Share your thoughts below or explore more math learning tools on StudyFriend.me — your AI-powered study companion.