6: Area and Perimeter

Last updated
Save as PDF

Page ID: 34145

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Area is the quantity that expresses the extent of a two-dimensional figure or shape in the plane. A perimeter is a path that encompasses/surrounds a two-dimensional shape. The term may be used either for the path, or its length—in one dimension. It can be thought of as the length of the outline of a shape. The perimeter of a circle or ellipse is called its circumference.

6.1: The Area of a Rectangle and Square
The measurement of the area of geometric figures is one of the most familiar ways mathematics is used in our daily lives. The floor space of a building, the stae of a picture, the amount of paper in a roll of paper towels are all examples of Items often measured in terms of area. In this chapter we will derive formulas for the areas of the geometric objects which we have studied.
6.2: The Area of a Parallelogram
The base may be any side of the parallelogram, though it is usually chosen to be the side on which the parallelogram appears to be resting. The height is a line drawn perpendicular to the base from the opposite side.
6.3: The Area of a Triangle
The base can be any state of the triangle though it is usually chosen to be the side on which the triangle appears to be resting. The height is the line drawn perpendicular to the base from the opposite vertex. Note that the height may fall outside the triangle, If the triangle is obtuse, and that the height may be one of the legs, if the triangle is a right triangle.
6.4: The Area of a Rhombus
The area of a rhombus can be found by using the formula for the area of a parallelogram, A=bh, since a rhombus is a special kind of parallelogram.
6.5: The Area of a Trapezoid
The area of a trapezoid is given by (a + b)h/2 where a and b are the lengths of the parallel sides, h is the height (the perpendicular distance between these sides).

Thumbnail: A parallelogram split into two equal triangles. (Public Domain; Jim.belk via Wikipedia)