How to Calculate the Area of a Two Dimensional Object

Working with mathematics isn't difficult, it's elementary.

For some people, math isn't always fun, but it can be useful. Finding the area of a 2-D object, such as a triangle or a rectangle, can be essential for those looking to tile a kitchen, build a deck or bake a cake. Use these basic formulas to solve your foundational mathematics problems, and don't worry, using a calculator won't count against you.

Things You'll Need

• Calculator (Optional)

Instructions

1. A Square:

   Multiply the height and width of the square to find the area.

   Area = h x w

   So that if a square has both height and width of size 5, the area would be 5 x 5 = 25.

2. A Rectangle:

   Multiply the height by the width.

   Area = h x w

   So that if a rectangle has a height of size 7 and a width of size 3, the area would be 7 x 3 = 21.

3. A Triangle:

   Multiply half of the base (the bottom of the triangle) by the height.

   Area = 1/2 b x h

   So that if a triangle has a base of size 10 and a height of size 13, the area would be 1/2 (10) x 13 = 5 x 13 = 65.

4. A Circle:

   Square the circle's radius (the length from the center of the circle to its edge) and multiply it by pi (symbolized in Greek as π).

   Area = πr^2 or π x r x r

   So that if a circle has a radius of 5, the area would be π x (5 x 5) ≈ 3.14 x 25 ≈ 78.5.

5. An Ellipsis:

   Halve the ellipsis vertically and horizontally so that the height of the ellipsis is h and the width of the ellipsis is w. Multiply 1/2 h by 1/2 w and then the whole thing by pi (π).

   Area = 1/2w x 1/2h x π

   So that if an ellipsis has a width of 10 and a height of 6, the area would be 1/2(10) x 1/2(6) x π ≈ 5 x 3 x 3.14 ≈ 47.1.

6. A Sector:

   Multiply 1/2 the square of the radius by the angle of the sector -- a piece of a circle, or a slice of the circle's pie shape -- to find its area.

   Area = 1/2r^2θ, where θ is the Greek theta, which stands for the angle in radians, which is a unit of angular measurement.

   So that if a sector has a radius of 3 and an angle of 45, the area would be 1/2(3^2) x 45 = 1/2(9) x 45 = 4.5 x 45 = 202.5.

7. A Parallelogram:

   Multiply the base (bottom of the object) by the height from the base to the top of the object. A parallelogram is a skewed rectangle.

   Area = b x h

   So if you have a parallelogram of base 5 and vertical height 3, the area would be 5 x 3 = 15.

8. A Trapezoid:

   Multiply half of the sum of the top, a, of the object and the base (or bottom), b, by the vertical height, h. A trapezoid has four sides with two sides equal and two other sides of non-equal measures.

   Area = 1/2(a + b) x h

   So that if a trapezoid has a top measure of 4, a base of 6 and a vertical height of 5, the area would be 1/2(4 + 6) x 5 = 1/2(10) x 5 = 5 x 5 = 25.

Tips & Warnings

• From here, finding the area of complex 2-D objects can be broken into pieces, with each shape within the object's overall outline containing its own formula.

• Remember the order of operations when computing areas: perform square roots and parentheses first, then multiplication and division, then addition and subtraction, in that order, from left to right.

• Most calculators need parentheses to help with order of operations. If your calculator doesn't have this feature, be careful when inputting numbers.

References

• Math.com: Area Formulas