What is a Trapezoid?
Trapezoid is a 2D shape that is a four sided polygon or a quadrilateral where any one pair of opposite sides are always parallel.
ABCD is a 4 sided trapezoid, where AB and CD are parallel sides, and h is the height.
Area of such a shape is given by half times, product of sum of parallel sides and height.
A = ½ (a +b) h , where AB = a and CD = b
Note: It is possible that one of the angles of a trapezoid is a right angle.
How to use Trapezoid:
When we come across surfaces of objects similar to trapezoids, as in the case of table lamps, face of frustum of a cone or a bucket or funnel, we can use the trapezoid to represent the diagram.
Area of trapezoidal shapes can be found out using the area formula. Also, if area and sum of parallel sides are known, we can find the height.
Sample Math Problems
Question 1: Find the area of the trapezoid whose parallel sides are 9 and 12 cm respectively, and the non parallel sides are 4 and 5 cm.
Answer:
Since height is not given, we can't use the formula directly.
If we split the trapezoid into parallelogram and triangle, by drawing a line parallel to 4 cm side, sides of parallelogram are 4cm and 9cm.
Sides of the remaining triangle will be 12-9= 3cm , 4cm and 5cm.
Area of trapezoid = area of parallelogram + area of triangle
= base x height + ½ x base x height
= 9 x 4 + ½ x 3 x4 = 42 sq cm
Question 2: Find the missing angle in the following trapezoid
Answer:
360 - ( 105 +75 +78) = 102 degree
Question 3: Find the distance between parallel sides of the trapezoid, if the sum of their parallel sides is 23 cm and the area is 92 sq cm.
Answer: Area = 92 = ½ x (23) x h => h = 8 cm.
Question 4: Find the area of a trapezoid whose parallel sides are 8 and 10 cm respectively, and the height is 5 cm.
Answer: ½ x (8+10) x 5 = 45 square cm.
