The area of a plane figure is the space enclosed by the plane figure. In other words, the area is the amount of space the plane figure takes in a two-dimensional plane.
For some plane figures such as rectangles, squares, triangles, and trapezoids, it may be easier to count the number of square units they enclose. However, for circles and ellipses, things get more complicated and special techniques are required to get accurate answers.
The figure above has the following 3 plane figures:
Trapezoid = rectangle + triangle
Suppose each square is equal to 1 square unit. To find the area of the rectangle, count the number of square units inside the rectangle.
Since the rectangle has 40 square units, the area is 40 square units.
It is not easy to count the number of square units inside the triangle. However, the space enclosed by the triangle is half the space enclosed by the rectangle.
Looking at our figure above, we see that the area of the trapezoid is equal to the area of the rectangle plus the area of the triangle.
Area of the trapezoid = 40 + 20 = 60
There is another way to get 60 although it is not easy to notice.
Just take the average of the parallel sides of the trapezoid and multiply the answer by the height of the trapezoid, which is the same as the height of the rectangle or triangle in this case.
One of the parallel sides (top one) is equal to 5 and the other (bottom one) is equal to 10.
[(5 + 10)/2] × 8 = (15/2) × 8 = 7.5 × 8 = 60
The area of a circle is area = πr2 and it is not as easy to show by counting square units. Here is a proof of the area of a circle.