Intermediate · 12 min
Circles and right triangles
Calculate circle measurements and find missing sides of right triangles.
Distinguish radius and diameter
The diameter is twice the radius. A circle's circumference is 2πr and its area is πr². Keep length and area units separate.
Worked example
For radius 3 and π ≈ 3.14: circumference ≈ 18.84; area ≈ 28.26.
Use Pythagoras for a right triangle
The square of the hypotenuse equals the sum of the squares of the two shorter sides. The hypotenuse is opposite the right angle.
Worked example
Shorter sides 3 and 4 give c² = 9 + 16 = 25, so c = 5.
Compare lengths
- Find the diagonal of a rectangle with sides 5 and 12.
- Explain why its diagonal is the hypotenuse of a right triangle.