Understanding Area in Math

Study Notes

A two-dimensional geometric shape is a flat shape, such as a drawing or a picture.
The definition of area in math is the space inside of the shape.
The area of a two-dimensional shape is a measurement of the space inside the shape.
The area of a two-dimensional shape is measured in square units, or units2.

The formula for finding the area, A, of a square with side length s is: A = s²
The formula for finding the area of a rectangle with length l and width w is: A = l × w
The formula for finding the area of a triangle with base b and vertical height h is: A = (b × h) / 2
The formula for finding the area of a circle with radius r is: A = π × r²
The formula for finding the area of a parallelogram with base b and vertical height h is: A = b × h
The formula for finding the area of a trapezoid with bases a and b and vertical height h is: A = ((a + b) × h) / 2
The formula for finding the area of an ellipse with major axis radius a and minor axis radius b is: A = π × a × b

Not every shape has an area formula.
The basic area formulas can be used to calculate the area of many uncommon shapes.
The area of an uncommon shape can be found by dividing the shape into more basic shapes.

Example 1: Find the area of a circle with a radius of 5 inches.
- The area of the circle is approximately 78.5 square inches.
Example 2: Find the area of a triangle with base 8 cm and height 3 cm.
- The area of the triangle is 12 square centimeters.
Example 3: Find the area of a shape made up of a rectangle and a triangle.
- The area of the shape is 55 square inches.
Example 4: Find the area of the shaded region of a shape.
- The area of the shaded region is approximately 72 square centimeters.