Geometry – Area of a Triangle, Square and other Shapes

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      The area of a shape can be understood if we try to imagine how many little squares are needed to cover a shape. 

     For example, we can think of area as the number of square tiles that fit evenly on a floor, or the number of rectangles that fit side by side in an interlocking driveway, that is area. 

     Area can be measured in square feet, square meters (metres), and square inches (or in metric centimeters) etc….  We always express area as units squared (²).

     Younger students are usually given graph paper whereby they calculate the area of a shape by adding up the squares inside.  Older students use formulas (formulae) to calculate area.  All polygons and circles have a formula for finding their area.

Area of a Rectangle
The area of a rectangle is equal to the product (the result of multiplication) of the length of its base and the length of its height. The height is a segment that is perpendicular to the base. The base and height of a rectangle is also referred to as its length and width.

The formula for finding the area of a rectangle is: 

A = bh

Area = base x height

Area of a Square
Since a square is a rectangle; we can use the same formula to find its area.   But in a square, we don’t have a ‘width’ or a ‘length’ because all the sides are the same. The area of a square is equal to the length of one side squared.

The formula for finding the area of a square is:

A = s²

Area = side ²

Area of a Parallelogram
To find the area of a parallelogram, we can use the same formula that we used for the area of a rectangle.

The formula for finding the area of a parallelogram is: 

A = bh

Area = base x height

Area of a Triangle

Triangles can be regarded as a parallelogram with a diagonal line cutting through making two triangles.  The area of a triangle is therefore one-half the area of the quadrilateral, which is base length multiplied by the height.  To find the area of a triangle, we will use the formula of finding the area of a parallelogram, but, since the triangle is half of the parallelogram, we use the following formula:

A = ½ bh

Area = ½ base x height

Area of a Trapezoid
To find the area of a trapezoid, we can draw a diagonal so the trapezoid is divided into two triangles.  Now, we get two triangles that are not the same size.  So, we must find the area of each triangle and add the areas together.

A = ½ (base 1 + base 2) h

Area = ½ x base 1 + base 2 x height

Area of a Circle
In order to find the area of a circle, we use the following formula:

A = πr²

The ‘A’ represents the area. The symbol “π” is always 3.14. The ‘R’ stands for the radius (a line from any point on the outside of the circle to the centre).

     Clearly, some shapes share common characteristics whereby we can use the same or similar formula to find the area. 

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Tutorgiant.com provides Area lessons with worksheets.

See some of the lessons in our video library.

AREA - Lesson (A) Introduction to Area (Grades 1-2)
AREA - Lesson (B) Area of a Rectangle (Grade 4)
AREA - Lesson (C) Area of a Parallelogram (Grades 7-8)
AREA - Lesson (D) Area of a Circle (Grades 7-8)
AREA - Lesson (E) Area of a Triangle (Grades 7-8)
AREA - Lesson (F) Area of Trapezoids (Grades 7-8)
AREA - Lesson (G) Surface Area of Rectangular Prisms (Grades 7-8)
AREA - Lesson (H) Surface Area of Cylinders (Grades 7-8)
AREA - Lesson (I) Area of Complex Shapes (Grades 7-8)
AREA - Lesson (J) Surface Area of Cubes (Grades 7-8)

Learn'Em Good                 

       Math                  

by Stuart Ackerman        

     MSc.Ed.,B.A.