Which formula correctly calculates the area of a triangle?

Which formula correctly calculates the area of a triangle?

• A. A = 1/2 bh
• B. A = bh
• C. A = s^2
• D. P = a+b+c

Answer: (A)

The main idea is that a triangle’s area is half the product of its base and height. If you draw a rectangle with the same base and height, its area is base × height. The triangle that fits inside that rectangle with the same base and height covers exactly half of that rectangle, so the triangle’s area is (base × height) / 2. That’s why the correct formula is area = 1/2 × base × height. The other expressions don’t describe a triangle’s area: bh would be the rectangle area with that base and height, s^2 is the area of a square with side s, and the perimeter a + b + c sums the triangle’s side lengths.

The main idea is that a triangle’s area is half the product of its base and height. If you draw a rectangle with the same base and height, its area is base × height. The triangle that fits inside that rectangle with the same base and height covers exactly half of that rectangle, so the triangle’s area is (base × height) / 2. That’s why the correct formula is area = 1/2 × base × height.

The other expressions don’t describe a triangle’s area: bh would be the rectangle area with that base and height, s^2 is the area of a square with side s, and the perimeter a + b + c sums the triangle’s side lengths.