text: # ISEE Upper Level Math : How to find the area of a trapezoid
  
  ## Example Questions
  
  ### Example Question #1 : How To Find The Area Of A Trapezoid
  
  Note: Figure NOT drawn to scale.
  
  The above trapezoid has area . What is  ?
  
  Explanation:
  
  Substitute  in the formula for the area of a trapezoid:
  
  ### Example Question #1 : Trapezoids
  
  A trapezoid has height 20 inches. Its bases have sum 30 inches, and one base is 6 inches longer than the other. What is the area of this trapezoid?
  
  It cannot be determined from the information given.
  
  Explanation:
  
  You do not need to find the individual bases; their sum, , is . You can substitute  into the formula for the area of a trapezoid:
  
  square inches.
  
  Note that the fact that one base is  inches longer is not important here.
  
  ### Example Question #3 : How To Find The Area Of A Trapezoid
  
  Find the area of the above trapezoid if , , and .
  
  Figure not drawn to scale.
  
  Explanation:
  
  The area of a trapezoid is given by
  
  ,
  
  where  are the lengths of each base and is the altitude (height) of the trapezoid.
  
  ### Example Question #4 : How To Find The Area Of A Trapezoid
  
  A trapezoid has the base lengths of and . The area of the trapezoid is . Give the height of the trapezoid in terms of .
  
  Explanation:
  
  The area of a trapezoid is given by
  
  ,
  
  where  are the lengths of each base and is the altitude (height) of the trapezoid.
  
  ### Example Question #5 : How To Find The Area Of A Trapezoid
  
  In the following trapezoid  and . The area of the trapezoid is 54 square inches. Give the height of the trapezoid. Figure not drawn to scale.
  
  Explanation:
  
  The area of a trapezoid is given by
  
  ,
  
  where  are the lengths of each base and is the altitude (height) of the trapezoid.
  
  Substitute these values into the area formula:
  
  ### Example Question #6 : How To Find The Area Of A Trapezoid
  
  What is the area of the shaded portion of the above square?
  
  Explanation:
  
  Quadrilateral  - the shaded region - is a trapezoid with bases  and , and altitude . The area of the trapezoid can be calculated using the formula
  
  ,
  
  where  and  , and .
  
  The length of  can be found by setting  and  and applying the Pythagorean Theorem:
  
  Therefore,
  
  .
  
  Substituting: