Question

I need help with the question that says the area of the triangle is…. What is one way to write the equation?

Answer 1

`A = (bh)/(2)`

Explanation:

`A = (1)/(2)b \cdot h`

`A = (bh)/(2)`

Answer 2

A = b(h/2)

Explanation:

Any rewrite of the equation can make use of the commutative and associative properties of multiplication.

What are the properties of multiplication?

The commutative property of multiplication lets you change the order of the operands. The given equation can have any of 6 different orders of operands:

A = (1/2)bh = (1/2)hb = b(1/2)h = bh(1/2) = h(1/2)b = hb(1/2)

The associative property of multiplication lets you change the grouping of the operands:

A = ((1/2)b)h = (1/2)(bh)

These ways of grouping operands can apply to any of the 6 different orders of operands, so there are 12 ways to write the equation.

One way to write the equation is ...

A = b(h/2)

__

Additional comment

Please note that the way we have written the equation helps you see that the area of a triangle is equivalent to the area of a rectangle that has half the height. This can sometimes be useful when computing the areas of composite figures.

• A = bh . . . . . . . rectangle area
• A = b(h/2) . . . . triangle area with the same height