For a triangle with base b and height h, which expression gives the area?

For a triangle with base b and height h, which expression gives the area?

• A. base × height
• B. 1/2 × base × height
• C. 2 × base × height
• D. base ÷ height

Answer: (B)

Area of a triangle is found by taking half the product of its base and its height. If you think of a rectangle with the same base and height, its area is base × height. The triangle fits inside that rectangle and, when you split the rectangle along a diagonal, you get two equal triangles. Each triangle has half the area of the rectangle, so its area is (1/2) × base × height. That matches the expression one-half times base times height. For example, with base 6 and height 4, the area is 1/2 × 6 × 4 = 12 square units. The other expressions don’t give area: base × height would be the area of the full rectangle; 2 × base × height would double that area; base ÷ height isn’t an area and has incompatible units.

Area of a triangle is found by taking half the product of its base and its height. If you think of a rectangle with the same base and height, its area is base × height. The triangle fits inside that rectangle and, when you split the rectangle along a diagonal, you get two equal triangles. Each triangle has half the area of the rectangle, so its area is (1/2) × base × height. That matches the expression one-half times base times height.

For example, with base 6 and height 4, the area is 1/2 × 6 × 4 = 12 square units.

The other expressions don’t give area: base × height would be the area of the full rectangle; 2 × base × height would double that area; base ÷ height isn’t an area and has incompatible units.