Area of 2D Shapes
Lessons in this chapter
About Area of 2D Shapes
Area of 2D Shapes extends area beyond the rectangle, and every formula in it is derived from the rectangle rather than handed over.
Find the Area of Parallelograms shows the derivation that sets the pattern. Cut a triangle from one end of a parallelogram and move it to the other, and you have a rectangle of the same area, which is why the formula is base times height. The height is the perpendicular height, not the slanted side, and that is the error to watch for.
Find the Area of Triangles follows immediately. Two identical triangles make a parallelogram, so a triangle is half of base times height.
Find Area of Trapezoids and Kites continues the method. A trapezoid's area uses the average of the two parallel sides times the height, which is just the rectangle that would have the same area.
Find Area of Composite Figures applies the splitting strategy from 3rd grade to a wider set of shapes. Break the figure into shapes you have formulas for, find each area, and add, or sometimes subtract a piece that has been cut away.
All four lessons in Area of 2D Shapes open as 6th grade math worksheets in the page. Find the Area of Parallelograms, Find the Area of Triangles and Find Area of Composite Figures each give math problems worked one at a time and scored as you go, so a height read off the wrong side of a diagram shows up straight away. They are free to try, with no login needed for your first 3.
Frequently asked questions
Find the Area of Parallelograms starts by rearranging a parallelogram into a rectangle, which is where base times height comes from and why the height has to be perpendicular rather than the slanted side. Find the Area of Triangles follows from the same picture, a triangle being half a parallelogram, and Find Area of Trapezoids and Kites extends the idea to two more shapes. Find Area of Composite Figures then stops giving a formula at all, asking children to break an irregular figure into shapes they already know, or to subtract a piece from a larger rectangle. The chapter sits in the Common Core domain Geometry (6.G).
Base times perpendicular height. It works because cutting a triangle off one end and moving it to the other turns the parallelogram into a rectangle of the same area.
Because two identical triangles fit together to make a parallelogram. The triangle is half of it.
Using the slanted side instead of the perpendicular height. The height must be measured at a right angle to the base, and in a diagram it is often the shorter of the two.
Average the two parallel sides and multiply by the height. The average gives the width of a rectangle with the same area.
Split it into shapes you have formulas for and add the areas, or work out a larger shape and subtract the part that is missing.