Are (1/2 x 3) x 8 and 3 x (1/2 x 8) equal? Explain how this can help in finding the area of a triangle
Yes, (1/2 x 3) x 8 and 3 x (1/2 x 8) are equal. To understand why they are equal, we need to apply the associative property of multiplication. According to this property, the grouping of factors in a multiplication operation does not affect the final result.
Let's break down the expressions step by step:
(1/2 x 3) x 8 = (3/2) x 8 = 24/2 = 12
3 x (1/2 x 8) = 3 x (8/2) = 3 x 4 = 12
Both expressions simplify to 12, so they are indeed equal.
Now, let's see how this concept can help us find the area of a triangle. The formula to calculate the area of a triangle is:
Area = (base x height) / 2
Here, the base and height are the two sides of the triangle that meet at a right angle. If we have the base and height values, we can substitute them into the formula and solve for the area.
To understand this visually, imagine the triangle as a rectangle with its base and height. If we find the area of this rectangle, it will be twice the area of the triangle because the triangle only occupies half of the rectangle.
By using the associative property of multiplication, we can rearrange the formula as:
Area = (1/2 x base) x height
This is equivalent to the expression (1/2 x 3) x 8 or 3 x (1/2 x 8) that we discussed earlier. By plugging the appropriate values for the base and height into this expression, we can find the area of the triangle.