In this lesson, we give
Shape 
Area 
Perimeter 
Square 
s^{2} 
4s 
Rectangle 
lw 
2(l + w) 
Parallelogram 
lh 
2(l + w) 
Trapezoid 

a + b + c + d 
Triangle 
bh 
a + b + c 
Rhombus 

4s 
Kite 

2(l + w) 
Regular Polygon 

ns 
Circle 
πr^{2} 
2πr 
Ellipse 
πab 

The area of a square is equal to the length of one side squared.
Area of a square = s^{2}
How to find the area of a square?
The formula for the area of a square is s × s = s^{2}, where s is the length of a side of the square.
A rectangle is a 4sided 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
A parallelogram is a 4sided 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 = bh
How 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.
A trapeziod or trapezium is a 4sided 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.
A triangle is a 3sided polygon.
Area of triangle = × Base × Height
A = bh
The following video shows an example of using the formula of half the product of the base and height to calculate the area of a triangle.
Area of triangle = ab sin C
How to find the area of a triangle given sideangleside (SAS)?
We can find the area of the triangle using a formula that uses the sine function.
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 ahows how to use the Heron's Formula.
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
The following video gives the formula for the area of an equilateral triangle given the length of its side.
A rhombus is a 4sided 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 = a^{2} 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.)
Find the area of a rhombus given a diagonal and two angles.
What is the area of a rhombus that has two 120 degrees angle and a longer diagonal measuring 10 meters?
A kite is a 4sided 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
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?
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 = × (radius)^{2}
A = r^{2}
How to find the area of a circle given the radius or diameter?
A sector ia the portion of circle that is enclosed by two radii and an arc. The following video shows how to calculate the area of a sector in degrees.
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.
How to find the area of an ellipse given the lengths of the major axis and minor axis? 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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