How does (1/2 x 3) x 8 and 3 x (1/2 x 8) being equal help in finding the area of a triangle?
To understand how the expressions (1/2 x 3) x 8 and 3 x (1/2 x 8) being equal help in finding the area of a triangle, we need to understand the concept of finding the area of a triangle.
The area of a triangle can be calculated using the formula: A = (base x height) / 2.
In this formula, the base and height of the triangle are the two sides that intersect to form a right angle.
Now, let's look at the expressions (1/2 x 3) x 8 and 3 x (1/2 x 8):
(1/2 x 3) x 8 is equal to (0.5 x 3) x 8 which evaluates to 1.5 x 8 = 12.
3 x (1/2 x 8) is equal to 3 x (0.5 x 8) which evaluates to 3 x 4 = 12.
These two expressions are equal to 12, which means they represent the same value.
Now, let's relate this to the area of a triangle.
Imagine we have a triangle with a base of 3 units and a height of 8 units.
Using the formula A = (base x height) / 2 and substituting the values, we get A = (3 x 8) / 2 = 24 / 2 = 12.
This is the same value we obtained from the expressions (1/2 x 3) x 8 and 3 x (1/2 x 8).
Therefore, knowing that (1/2 x 3) x 8 and 3 x (1/2 x 8) are equal is helpful in finding the area of a triangle because it confirms the consistency of the formula used to calculate the area.