Explain how the area of a parallelogram is related to the area of a triangle when both figures have the same base and height
A triangle has half the area of a quadrilateral.
To understand how the area of a parallelogram is related to the area of a triangle when both figures have the same base and height, we first need to understand how to calculate the areas of these shapes.
The formula to find the area of a parallelogram is given by: Area = base × height. The "base" of a parallelogram is any of its sides, as long as it is parallel to the corresponding opposite side. The "height" of a parallelogram is the perpendicular distance between the base and the opposite side.
Similarly, the formula to find the area of a triangle is given by: Area = (base × height) / 2. Here, the "base" of a triangle is any one of its sides, and the "height" is the perpendicular distance from the base to the vertex opposite it.
Now, when a parallelogram and a triangle have the same base and height, it means that the base of the triangle is equal in length to one of the sides of the parallelogram, and the height of the triangle is the same as the height of the parallelogram.
Since the base and height are the same, we can rewrite the formula for the area of a parallelogram as: Area of Parallelogram = base × height.
Similarly, we can rewrite the formula for the area of a triangle as: Area of Triangle = (base × height) / 2.
In this case, when both figures have the same base and height, the area of the triangle will be half of the area of the parallelogram. This is because the formula for the area of a triangle includes dividing the product of the base and height by 2. So, mathematically, we can express this relationship as:
Area of Triangle = (Area of Parallelogram) / 2.
Hence, when the base and height are the same, the area of the parallelogram will always be twice that of the triangle.