Geometry: Areas of Polygons

Geometry Lessons: Areas of Polygons - square, rectangle, parallelogram, triangle, rhombus, trapezoid

The area of a polygon measures the size of the region enclosed by the polygon. This is usually expressed in terms of some square unit.

See also area of circles.

Areas of Squares

Area of a square = s²

Areas of Rectangles

Area of a rectangle = lw

Areas of Parallelograms

To get the area of a parallelogram, we first draw a perpendicular line segment from one corner of the parallelogram to the opposite side. This is the height ( h) of the parallelogram.

Area of a parallelogram = lh

You may notice that lh is also the area of a rectangle with dimensions l and h. The diagram below will explain why. If we cut out the triangle ABC and add it to the other side (triangle DEF), you will have a rectangle with dimensions l and h that has the same area as the original parallelogram.

Areas of Triangles

To get the area of a triangle, we first choose one of the sides to be the base ( b). Then we draw a perpendicular line segment from a vertex of the triangle to the base. This is the height ( h) of the triangle.

Areas of Rhombus

To get the area of a rhombus, we first draw a line segment from one vertex to another vertex ( b). Then we draw a perpendicular line segment from a third vertex to the base ( h). The rhombus consists of two triangles with base ( b) and height ( h).

Area of a rhombus = bh

Areas of Trapezoids

a is parallel to b

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