Which expression represents the area of a triangle with base b and height h?

Which expression represents the area of a triangle with base b and height h?

• A. bh
• B. 1/2 bh
• C. 2 bh
• D. b^2 h

Answer: (B)

The area of a triangle is found by taking half of the product of its base and its height. This comes from imagining two triangles that form a rectangle with the same base and height; together they make the rectangle, so each triangle is half of the rectangle’s area. With base b and height h, that area becomes (1/2) × b × h. So the correct expression is (1/2) b h. The other ideas would give the full rectangle’s area (bh), a doubled amount (2bh), or an extra factor of b (b^2 h), which doesn’t match the way area scales with base and height for a triangle.

The area of a triangle is found by taking half of the product of its base and its height. This comes from imagining two triangles that form a rectangle with the same base and height; together they make the rectangle, so each triangle is half of the rectangle’s area. With base b and height h, that area becomes (1/2) × b × h.

So the correct expression is (1/2) b h. The other ideas would give the full rectangle’s area (bh), a doubled amount (2bh), or an extra factor of b (b^2 h), which doesn’t match the way area scales with base and height for a triangle.