how to find area of a polygon

Related Pages
Polygons
Expanse Of Polygons - Composition and Decomposition
Surface area Of Circles
More than Geometry Lessons

Area Of Polygons - Formulas

The area of a polygon measures the size of the region enclosed by the polygon. It is measured in units squared.

The following table gives the formulas for the area of polygons. Scroll downwards the page if y'all need more explanations most the formulas, how to use them every bit well as worksheets.

area of polygon formulas

Area Of A Square

The area of a square is equal to the length of one side squared.

square

Area of a square = s ⁱⁱ

Surface area Of A Rectangle

The area of a rectangle" is equal to the product of the length of its base and the length of its peak. Sometimes, the height is called the "distance". Nosotros tin likewise call the longer side the "length" and the shorter side the "width"

rectangle

Surface area of a rectangle = lw

Worksheet 1, Worksheet 2, Worksheet 3 to summate the area and perimeter of rectangles.

Area Of A Parallelogram

parallelogram

To go the area of a parallelogram, we beginning draw a perpendicular line segment from 1 corner of the parallelogram to the reverse side. This is the height (h) of the parallelogram. The area of a parallelogram is equal to the production of its length and height. (Think to always use the perpendicular height.)

Expanse of a parallelogram = lh

You may notice that lh is also the surface area of a rectangle with dimensions l and h. The diagram below volition explain why. If we cutting out the triangle ABC and add it to the other side (triangle DEF), y'all volition have a rectangle with dimensions l and h that has the aforementioned area as the original parallelogram.

area of parallelogram

Worksheet to calculate the expanse of parallelograms.

Area Of A Triangle

area of triangle

To get the area of a triangle, we first cull ane of the sides to be the base (b). So nosotros depict a perpendicular line segment from a vertex of the triangle to the base. This is the height (h) of the triangle. The area of a triangle is equal to half the production of the base of operations and the height.

At that place are too other formulas for the expanse of a triangle. More than examples, formulas and videos for area of triangles

Area Of A Rhombus

Nosotros tin can obtain the surface area of a rhombus, given the lengths of its diagonals.

area of rhombus

If the lengths of the diagonals are a and b , and then expanse of the rhombus is equal to half the production of the diagonals.

Area of rhombus =

If you lot are given the length of one side (s) and the perpendicular height (h) from 1 side to the vertex then the area of the rhombus is equal to the product of the side and acme.

The area of the rhomb is given by the formula:

Area of rhombus = sh

This formula for the area of a rhombus is similar to the area formula for a parallelogram.

Area Of A Kite

The area of a kite uses the same formula every bit the expanse of a rhombus. The area of a kite is equal to half the product of the diagonals.

Expanse of kite =

Area Of A Trapezoid

area of trapezoid

a is parallel to b

To become the area of a trapezoid, nosotros sum the length of the parallel sides and multiply that with half of the acme. Remember that the height needs to exist perpendicular to the parallel sides.

Worksheet to summate area of polygons.

The following video gives formulas and examples to find the area of squares, rectangles, triangles, parallelograms, and trapezoids. It also explains the divergence between base and height.

Bear witness Video Lesson

How to derive the area formula of a kite and a rhombus based on the rectangle formula?
How to calculate the area of a rectangle using diagonal lengths?

Show Video Lesson

Area Of Any Regular Polygon

A regular polygon is a polygon where all the sides are the aforementioned length and all the angles are equal.

area of polygon with apothem

How to observe the area of a regular polygon?

The apothem of a regular polygon is a line segment from the center of the polygon to the midpoint of 1 of its sides. The area of any regular polygon is equal to half of the product of the perimeter and the apothem.

Area of regular polygon = wherep is the perimeter andais the apothem.

How to utilise the formula to notice the area of any regular polygon?

Show Video Lesson

Try the gratis Mathway computer and problem solver beneath to practise various math topics. Try the given examples, or type in your own problem and check your respond with the step-by-step explanations.
Mathway Calculator Widget