Hello! Today we're going to learn about finding the area of parallelograms and trapezoids. These are special shapes that we can transform into rectangles to make calculating their area much easier. Let's start with the parallelogram, which has a base b and height h.
Now let's see the magic! We can transform a parallelogram into a rectangle by cutting off the triangle on the right side and moving it to the left side. This doesn't change the area at all! The rectangle has the same base b and height h, so the area formula is base times height.
Now let's look at trapezoids! A trapezoid is a special shape with two parallel sides called bases. The longer base at the bottom is called b, the shorter base at the top is called a, and the perpendicular distance between them is the height h. Notice the parallel marks that show which sides are parallel.
Here's a clever trick! If we take two identical trapezoids and flip one upside down, we can arrange them to form a parallelogram. The parallelogram has a base of a plus b and height h. Since the parallelogram contains two trapezoids, one trapezoid's area equals half the parallelogram's area. So the trapezoid area formula is a plus b times h, all divided by 2.