Remember some basic facts: area of a parallelogram is base length and height. Since a rectangle is a type of parallelogram its area is also base length times height, but the height of a rectangle is its width, and the base length is just called length, so the area is usually length times width.
A triangle is half a parallelogram so it has half the area of a parallelogram making its area ½base times height.
A trapezoid consists of two triangles and a rectangle, so if you can't remember the formula for the area of a trapezoid you can use the fact that you know how to find the area of a rectangle and a triangle. Just draw a sketch of the trapezoid by drawing a rectangle (forming the centre of the trapezoid) and add the triangular "wings". The height (width) of the rectangle is the same height as the two end triangles.
Its also important to know that the area of a circle is πr2 where r is the radius. If you cut a circle as would a pie you can find the area of a sector (piece of pie) by simple proportion. The angle at the centre of the circle is the apex angle of the sector, so the ratio of the area of the sector to the area of the circle is the same as the ratio of the angle of the sector to 360 degrees or 2π radians. For example, if a pie is cut into quarters the angle of the sector is 90° (quarter of 360° or ¼(2π)=π/2 radians) and the area is a quarter of the area of a circle=¼πr2. π is often given as a number: 3.14 or 22/7. Most calculators have a π (pi) button.
Knowing these simple basic facts can help you to find the area of other shapes, like polygons, which are made up of rectangles, circles (sectors, semicircles, etc.) and/or triangles. So you work out the areas of the various familiar shapes and then add them all together. Best to draw a sketch of the figure you're trying to find the area of, and adding extra lines if necessary so that you can see the familiar figures which you already know how to find the areas of.
