Area

 Introduction

Area is a quantity expressing the two dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The surface area of a 3 dimensional solid is the total area of the exposed surface, such as the sum of the areas of the exposed sides of a polyhedron. Area is an important invariant in the differential geometry of surfaces.

The area of a figure measures the size of the region enclosed by the figure. This is usually expressed in terms of some square unit. A few examples of the units used are square meters, square centimeters, square inches, or square kilometers.

Area of a Square

If l is the side length of a square, the area of the square is l² or l * l

Area of a Rectangle

The area of a rectangle is the product of its width and length.

Area of a Parallelogram

The area of a parallelogram is b * h, where b is the length of the base of the parallelogram, and h is the corresponding height. To picture this, consider the parallelogram below:

We can picture cutting off a triangle from one side and pasting it onto the other side to form a rectangle with side lengths b and h. This rectangle has area b * h.

The figure formed is a parallelogram having an area of h * (a + b), which is twice the area of one of the trapezoids.

Example:

If a and b are the lengths of the two parallel bases of a trapezoid, and h is its height, the area of the trapezoid is 1/2 * h * (a + b) . To picture this, consider two identical trapezoids, and turn one around and paste it to the other along one side as pictured below:

The figure formed is a parallelogram having an area of h * (a + b), which is twice the area of one of the trapezoids.

Area of a triangle = 1/2bh Area of a circle = πr²