Area is the number of square units inside of a shape. We typically find the area of a shape that is two dimensional (like a floor, or a piece of carpet, or a piece of land).
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Since the area is measuring the number of square units inside of the shape, the units must be written as squared units (ex: cm2).
Many of the area formulas require you to know the height of the shape.
The height of the shape is always the distance from the top of the shape to the bottom. The height must be a straight, vertical line.
Keep this page handy as you study formulas and solve real world problems throughout your algebra studies!
Area of a Square
A square has 4 sides that are all exactly the same size. Therefore, finding the area is pretty easy! Since the area of a square or rectangle is length x width, we can just square the length of the side! Take a look!
Area of a Rectangle
A rectangle is a 4 sided figure with two pairs of parallel lines. Each set of parallel lines has the same length. To find the area of a rectangle we are going to multiply the length x the width.
Area of a Parallelogram
A parallelogram is another 4 sided figure with two pairs of parallel lines. To find the area of a parallelogram, we will multiply the base x the height. Let's look at the formula and example.
Notice that we did not use the measurement of 4m. 4m did not represent the base or the height, therefore, it was not needed in our calculation.
Area of a Trapezoid
A trapezoid is a 4 sided figure formed by one pair of parallel sides. This area formula is a little more complicated. Study the example carefully!
Take note that the bases of a trapezoid are always the parallel lines.
Area of a Triangle
A triangle is a 3 sided figure. There are several different types of triangles. You must be careful when trying to locate the height of the triangle. Remember the height of the shape must be a straight, vertical line.
Again, notice that we did not need to use the measurement of 11cm. 11cm did not represent the base of the triangle, nor did it represent the height.
** You will not always need to use every measurement that is given in the problem.
Area of a Circle
A circle, of course, has no straight lines. We use pi (3.14) when we calculate the area of a circle.
What Would Happen if We Were Given the Diameter of the Circle and Asked to Find the Area?
f you are given the diameter of a circle (which is the distance across the circle - through the center), then you would divide the diameter in half. One-half of the diameter = the radius.
Don't forget that the area is a measurement of the inside space of a two dimensional figure. We are measuring how many 'square units' fit on the inside.
I hope that these formulas have helped you to solve your algebra problems. Good luck!
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In these lessons, we have compiled
- a table of area formulas and perimeter formulas used to calculate the area and perimeter of two-dimensional geometrical shapes: square, rectangle. parallelogram, trapezoid (trapezium), triangle, rhombus, kite, regular polygon, circle, and ellipse.
- a more detailed explanation (in text and video) of each area formula.
Area of a Square
The area of a square is equal to the length of one side squared.
Area of a square = s2
How to find the area of a square?The formula for the area of a square is s × s = s2, where s is the length of a side of the square.
- Show Step-by-step Solutions
Area of Rectangle
A rectangle is a 4-sided polygon where all four of its angles are right angles. Normally, the longer side is called the length and the shorter side is called the width. If all the sides are of equal length then it will be called a square.
Area of rectangle = length × width
A = lw
Area of Parallelogram
A parallelogram is a 4-sided polygon that has two sets of parallel sides. The opposite sides of a parallelogram are of equal length and the opposites angles are equal.
Area of parallelogram = base × perpendicular height
A = bhHow to find the area of a rectangle, triangle and parallelogram, using base and height?Always use the height that is perpendicular to the base. Do not use the slant height.
Area of Trapezoid / Trapezium
A trapezoid or trapezium is a 4-sided polygon that has at least one pair of parallel side. It is called a trapezoid in North America and a trapezium in Britain and other countries.
Area of trapezium = × (sum of two parallel sides) × height
A = × (a + b) × h
How to find the area of a trapezoid?Remember to use the height that is perpendicular to the base.
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Area of Triangle (given base and height)
A triangle is a 3-sided polygon.
Area of triangle = × Base × Height
Basic Area Formulas
A = bh
How to use the formula of half the product of the base and height to calculate the area of a triangle?Area of Triangle (given 2 sides and an included angle)
Area of triangle = ab sin C How to find the area of a triangle given side-angle-side (SAS)?We can find the area of the triangle using a formula that uses the sine function.
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Area of Triangle (given 3 sides)
Area of triangle =
This is also called the Heron's Formula
How to find the area of a triangle given the 3 sides?The following video shows how to use the Heron's Formula.
Area of an Equilateral Triangle
To find the area of an equilateral triangle, we can use the following formula:
The area of an equilateral triangle (with all sides congruent) is equal to
where s is the length of any side of the triangle
Given side of length s, the area of an equilateral triangle is s-squared times the square root of three over four.
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Area of Rhombus (given the length of the diagonals)
A rhombus is a 4-sided polygon that has 4 equal sides. The diagonals of a rhombus bisects each other at right angles.
Area of rhombus = product of diagonals
Area of Rhombus (given length of side and an angle)
Basic Geometry Area Formulas
Area of rhombus = a2 sin c where a is the length of the side and c is any interior angle.
(You can use any interior angle because either they are equal or they are supplementary and supplementary angles have the same sine.)
Example:
What is the area of a rhombus that has two 120 degrees angle and a longer diagonal measuring 10 meters?
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Basic Area Formulas Pdf
Area of Kite (given the length of the diagonals)
A kite is a 4-sided polygon that has two distinct pairs of adjacent sides that are congruent.. The diagonals of a kite bisects each other at right angles.
Area of a kite uses the same formula as the area of a rhombus
Area of kite = product of diagonals
Area of Regular Polygon
A regular polygon is a polygon where all the sides are the same length and all the angles are equal.
The apothem of a regular polygon is a line segment from the centre of the polygon to the midpoint of one of its sides.
Area of regular polygon = where p is the perimeter and a is the apothem.
How to find the area of a regular polygon, given the apothem and the length of the side?Area of Circle
A circles is a shape consisting of those points in a plane which are at a constant distance, called the radius, from a fixed point, called the center.
Area of circle = π × (radius)2
A = πr2
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Area of Sector
A sector is the portion of circle that is enclosed by two radii and an arc.How to calculate the area of a sector in degrees?
Area of Ellipse
An ellipse is a curved line forming a closed loop, where the sum of the distances from two points (foci) to every point on the line is constant. It looks like a circle that has bee squashed into an oval.
If 2a and 2b are the lengths of the major and minor axes of the ellipse, then the area of the ellipse is πab.
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