Find a
a² = 13² − 12²
a = 5
Pythagorean Theorem Challenge
Explore right triangles, discover how the theorem works, and solve geometry challenges.
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Explore the Pythagorean Theorem
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What Is the Pythagorean Theorem?
In every right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.
a² + b² = c²
What Is It Used For?
It helps you find a missing side of a right triangle. You can use it to calculate diagonals, distances, and lengths in geometry and real-life problems.
How Does This Picture Show It?
The two smaller squares contain geometric pieces that can be rearranged to fill the larger square on the hypotenuse.
The pieces preserve their area as they move and rotate. Their combined area illustrates a² + b² = c².
Find the Missing Side
Use the Pythagorean theorem to find a, b, or c. The hypotenuse c is always opposite the right angle. To find a leg, subtract the other leg’s square from the hypotenuse’s square.
Find b
b² = 17² − 8²
b = 15
Find c
c² = 9² + 12²
c = 15
Triangles in Shapes
Find right triangles hidden inside larger shapes. You will need to know the properties of squares, isosceles trapezoids and parallelograms, as well as the Pythagorean theorem. Each answer unlocks the next calculation.
Isosceles Trapezoid
Step-by-Step Solution
1 · Find A
In an isosceles trapezoid, the two legs are equal. The known leg is 13, so a = 13.
2 · Find B
Subtract the upper base from the lower base, then divide by two.
b = (19 − 9) ÷ 2 = 5
3 · Find C
Use the right triangle at the side of the trapezoid. Side a is the hypotenuse.
c = √(13² − 5²) = 12
4 · Find D
Use the blue right triangle. Its legs are c and the upper base, so d is the hypotenuse.
d = √(12² + 9²) = 15
Every answer is a whole number.