A right triangle has legs 3 and 4. What is the area of the triangle?

A right triangle has legs 3 and 4. What is the area of the triangle?

• A. 4
• B. 3
• C. 6
• D. 12

Answer: (C)

The area formula for a triangle uses base times height, then halves the result. In a right triangle, the two legs are perpendicular, so they act as base and height. With legs measuring 3 and 4, the area is 1/2 × 3 × 4 = 6. This also matches thinking of the triangle as half of a 3 by 4 rectangle (whose area is 12). The lengths 3 or 4 are side lengths, not areas, and 12 would be the area of the full rectangle, not the triangle.

The area formula for a triangle uses base times height, then halves the result. In a right triangle, the two legs are perpendicular, so they act as base and height. With legs measuring 3 and 4, the area is 1/2 × 3 × 4 = 6. This also matches thinking of the triangle as half of a 3 by 4 rectangle (whose area is 12). The lengths 3 or 4 are side lengths, not areas, and 12 would be the area of the full rectangle, not the triangle.