Geometry: Area

On this page we hope to clear up problems that you might have with area of polygons. The way it is laid out is as follows: Throughout our math experience, we have found it would be nice to have a comprehensive listing of all the different formulas you need to know to find the area of polygons. We have done that with significant addition — figures that help make the formula actually make sense! Read on or follow any of the links below to start understanding how to find the area of polygons!

Rectangles
Squares
Triangles
Parallelograms
Rhombuses
Trapezoids
Circles
Other
Quiz on area

Rectangles

Rectangle Area Postulate
The area A of any rectangle is equal to the product of the length l and the width w.

Formula: A = lw
Example: Example Figure

Squares

Square Area Theorem
The area A of any square is equal to the square of the length s of a side.

Formula: A = s^2
Example: Example Figure

Triangles

Triangle Area Theorem
The area A of any triangle is equal to one-half the product of any base b and corresponding height h.

Formula: A = .5bh
Example: Example Figure

Parallelograms

Paralleogram Area Theorem
The area A of any parallelogram is equal to the prodcut of any base b and the corresponding height h.

Formula: A = bh
Example: Example Figure

Rhombuses

Rhombus Area Theorem
The area A of any rhombus is equal to one-half the product of the lengths d1 and d2 (the variables would be subscripted if text-only browsers allowed for subscripted text) of its diagonals.

Formula: A = .5(d1)(d2)
Example: Example Figure

Trapezoids

Trapezoid Area Theorem
The area A of any trapezoid is equal to one-half the product of the height h and the sum of the bases, b1 and b2 (the variables would be subscripted if text-only browsers allowed for subscripted text).

Formula: A = .5h(b1 + b2)
Example: Example Figure

Circles & Sectors

Circle Area Postulate
The area A of any circle is equal to the product of PI and the sqaure of the radius r.

Formula: A = (PI)r^2
Example: Example Figure

Sector Area Theorem
The area A of any sector with an arc that has degree measure n and with radius r is equal to the product of the arc's measure divided by 360 multiplied by PI times the square of the radius.

Formula: A = (n/360)((PI)r^2)
Example: Example Figure

Other Polygons

Regular polygons are any polygons that are equilateral and equiangular.

Regular Polygon Area Theorem
The area A of any regular polygon with perimeter P and apothem of measure a is equal to one-half the product of the perimeter and the apothem.

Formula: A = .5aP
Example: Example Figure

Take the quiz on area. The quiz is very useful for either review or to see if you've really got the topic down.

Back
Site Map
Home
Next