Plane Figures

Plane figures are flat (2-dimensional) shapes.  Typically, you may be asked to find the area or perimeter of these shapes, and your formula sheet will help you.  Sometimes word problems will describe a shape and ask you to find its area or perimeter.  It may be helpful to draw out the shape on your whiteboard.




Perimeter of a shape is the distance around the outside of it.  Examples of problems that use perimeter are ones where you are making a frame around a picture or a fence around a yard.  Perimeter is measured in distance (meters, inches, feet, etc.)




Area is a measure of the size of a flat surface.  Problems where you have to find the area of a shape include mowing a lawn or painting a wall.  Area is measured in distance squared (square meters, square inches, square feet etc.)




Quadrilaterals are four sided shapes.  Squares, rectangles, parallelograms and trapezoids are all types of quadrilaterals.  The four angles in a quadrilateral add up to 360°.




A square is a four sided shape with four 90° angles and all four sides the same.  Because the sides are the same, to find the perimeter, the formula is p = 4s, which means perimeter equals 4 times the length of a side.  The area is a side squared.





Rectangles are quadrilaterals that have four 90° angles.  The sides opposite each other in a rectangle are equal in length and parallel.  A square is a type of rectangle.  To find the perimeter of a rectangle, the formula is p = 2l + 2w, or the perimeter is 2 times the length plus 2 times the width.  The formula for the area of a rectangle is A = lw, or the length times the width.




Parallelograms are quadrilaterals with the opposite sides equal in length and parallel.  The opposite angles in a parallelogram are also equal.  To find the perimeter of a parallelogram, use the same method as a rectangle- 2 times the length plus two times the length of the other side.  To find the area, use the formula A = bh, or area equals base times height.  Remember that the height of a parallelogram is not the length of one of the sides, but the distance between the two base sides.




Trapezoids are quadrilaterals in which two sides are parallel.  That is their only rule; al four sides can be different lengths and all four angles can be different as long as they all add up to 360°.  The formula for area of a trapezoid is A = h(b1 + b2), area is  times the height times the sum of the two bases.  The two bases are the two parallel sides, and the height is the distance between them.  You do not have a formula for perimeter of a trapezoid because all the sides are different, so you need to add up all four of them.


Pi (π)


Pi (π) is a number that is part of the relationship between the diameter and circumference and area.  The decimal places in pi go on forever, but for the purposes of the GED, pi is rounded off to 3.14.




A circle is a round figure with a center point.  The center is an equal distance from all points on the outside edge.  The radius of a circle is the distance from the center to the edge of a circle.  The diameter of a circle is the distance across a circle through the center.  The diameter is twice the length of the radius. 


To find the circumference, or perimeter of a circle, us the formula c = πd.  Or circumference equals pi times the diameter.  The formula sheet also lists this formula as 2πr, or 2 times pi times the radius, since the diameter is twice the radius.  To find the area of a circle, use the formula a = πr2, or area equals pi timed the radius squared.  Make sure when you use a formula for a circle that you are not using the diameter when the formula calls for the radius.