Area of 2-D ShapesA series of free High School Geometry Video Lessons from Brightstorm.
Area of Parallelograms The area of parallelograms formula is derived from the area of a rectangle. By drawing an altitude from one vertex in a parallelogram and translating the right triangle, a rectangle is formed. Therefore, to calculate the area of a parallelogram, multiply a height by the corresponding base. The corresponding base is the side perpendicular to the height. Related topics include area of trapezoids and rhombuses.
Area of Triangles The formula for calculating the area of triangles comes from dividing a parallelogram in half, so the area is half of base times height. When finding the area of a triangle, the height is an altitude and the base must be the side intersected by the altitude. When given the area and asked for a base or height, a common mistake is to forget to multiply both sides of the equation by 2 before dividing.
Area of Trapezoids The area formula for a trapezoid is found by making a parallelogram made up of two congruent trapezoids. To do this, copy a trapezoid, rotate the copy 180 degrees, and translate to create a parallelogram. The area of a parallelogram is base times corresponding height; since there are two trapezoids, the area of trapezoids formula must be divided in half. Since the bases are not congruent, they must be summed separately.
Solving Formulas Solving formulas for a variable is a critical skill in the Geometry area unit because many problems will give the area of a polygon and ask for a side, height, or some other dimension. In these cases, simply substituting and typing into a calculator will not yield the correct answer. The successful Geometry student must be capable of substituting into a formula and then solving formulas for the one remaining variable.
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