Question

What is the area of a triangle where the height is `(5a + 2)` and the base is `(4a - 1)`?

Answer 1

See a solution process below:

Explanation:

The formula for the area of a triangle is:

`A = (hb)/2`

Where:

`A` is the area of the triangle

`h` is the height of the triangle from the base

`b` is the length of the base

Substituting the expressions from the problem gives:

`A = ((5a + 2)(4a - 1))/2`

To multiply the two terms in the numerator you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`A = ((color(red)(5a) + color(red)(2))(color(blue)(4a) - color(blue)(1)))/2` becomes:

`A = ((color(red)(5a) xx color(blue)(4a)) - (color(red)(5a) xx color(blue)(1)) + (color(red)(2) xx color(blue)(4a)) - (color(red)(2) xx color(blue)(1)))/2`

`A = (20a^2 - 5a + 8a - 2)/2`

We can now combine like terms:

`A = (20a^2 + [-5 + 8]a - 2)/2`

`A = (20a^2 + 3a - 2)/2`

Or

`A = (20a^2)/2 + (3a)/2 - 2/2`

`A = 10a^2 + 3/2a - 1`