Explain how the areas of a triangle and a parallelogram with the same base and height are related.
parallelogram = bh
triangle = bh/2
so, the triangle's area is 1/2 that of the parallelogram
To explain how the areas of a triangle and a parallelogram with the same base and height are related, we need to understand the formulas for calculating the areas of both shapes.
1. Triangle:
The formula to calculate the area of a triangle is given by:
Area = (base * height) / 2
2. Parallelogram:
The formula to calculate the area of a parallelogram is given by:
Area = base * height
Now, let's compare the formulas for the triangle and the parallelogram.
Both the triangle and the parallelogram have the same base and height.
In the case of the triangle, the area is calculated by multiplying the base and height, and then dividing by 2.
In the case of the parallelogram, the area is calculated by directly multiplying the base and height.
Since the parallelogram does not divide the product of base and height by 2, its area will always be twice that of the corresponding triangle with the same base and height.
In other words, the area of a triangle is half that of a parallelogram with the same base and height.
This relationship holds true for any triangle and parallelogram with the same base and height, regardless of their shape or size.
To understand how the areas of a triangle and a parallelogram with the same base and height are related, let's start by looking at the basic formulas for calculating the areas of these shapes.
1. Triangle: The area of a triangle is given by the formula A = (1/2) * b * h, where A represents the area, b represents the base length, and h represents the height.
2. Parallelogram: The area of a parallelogram is given by the formula A = b * h, where A represents the area, b represents the base length, and h represents the height.
Now, if a triangle and a parallelogram have the same base and height, it means their base lengths and height measurements are equal. Let's say the base length is 'b' and the height is 'h'.
For the triangle, its area can be calculated as A = (1/2) * b * h.
For the parallelogram, its area can be calculated as A = b * h.
Comparing these two formulas, we can see that the area of the parallelogram is twice the area of the triangle with the same base and height. This can be expressed mathematically as:
A(Parallelogram) = 2 * A(Triangle)
In other words, the area of a parallelogram is always twice the area of a triangle with the same base and height.
parallelogram = bh
triangle = bh/2
so, the triangle's area is 1/2 that of the parallelogram