Area of Right Triangles Practice Problems & Conceptual Mastery
In a right triangle, the two sides that meet at the 90° right angle are called legs. Because they meet at a right angle, they are already perpendicular to each other, acting directly as base and height: Area = ½ × leg₁ × leg₂.
📝 Worked Step-by-Step Example
1. Formula: A = ½ × a × b. 2. Substitute: A = ½ × 9 × 10. 3. Multiply: 9 × 5 = 45 cm².
🧠 Core Problem-Solving Strategies
1. The Two Legs are Base and Height
Never look for an altitude line inside a right triangle: the two legs forming the 90° square corner *are* the base and height.
2. Ignore the Slanted Hypotenuse
The hypotenuse (the longest side opposite 90°) is never part of the area formula unless solving with trigonometry.
3. Halve the Even Leg First
To make mental math easy, divide the even leg by 2 first, then multiply by the other leg: ½ × 6 × 7 = 3 × 7 = 21.
📖 Key Mathematical Terms & Vocabulary
Legs
Hypotenuse
❓ Frequently Asked Questions
Why is a right triangle's area exactly half a rectangle?
Drawing a diagonal across any rectangle splits it into two identical, congruent right triangles. Thus, each triangle has exactly half the rectangle's area: ½ × l × w!
Can the hypotenuse ever be used as the base?
Yes, but you would then need the perpendicular altitude drawn to the hypotenuse, which is usually harder to find than simply using the two legs.
How can I recognize which sides are the legs?
Look for the small square right-angle symbol. The two sides that touch that square symbol are the legs.
Continue Learning & Practicing Area of Right Triangles
Reinforce your understanding with printable worksheets, step-by-step guides, calculators, and speed games: