7th Grade - Area of Trapezoids

Introduction

  • A trapezoid or trapezium is a quadrilateral that has only one pair of opposite sides parallel.
  • These parallel sides are called bases and the remaining non-parallel sides are called legs.

  • There are two types of trapezoids:

1. Right Trapezoids: If one leg of a trapezoid makes a pair of right angles with the two bases, it is called a right trapezoid.

2. Isosceles Trapezoids: If the legs of a trapezoid are equal, it is called an isosceles trapezoid.

 

Area of Trapezoids

  • The area of a trapezoid is the region enclosed by its four sides.
  • The area of a trapezoid depends upon the measure of its bases and height.
  • If we know the length of the bases, and the height of a trapezium, we can determine its area using the formula mentioned below.

Areatrapezoid= b1+b22×h , where b1 and b2 are the length of bases, and h=height.

  • The perimeter of a trapezoid is the sum of the length of all its sides.

Some Solved Examples

Question 1: Find the area of the trapezium shown in the figure below.

Solution: Areatrapezoid=b1+b22×h=7+112×5=182×5=9×5=45 cm2

 

Question 2: Find the area of the trapezium shown in the figure below.

Solution: Areatrapezoid=b1+b22×h=5+102×6=152×6=15×3=45 m2

Cheat Sheet

  • The legs of an isosceles trapezoid are equal.
  • The perimeter of a trapezoid is the sum of all its sides.
  • Areatrapezoid=b1+b22×h, where b1,b2=length of bases, and h=height of the trapezoid

Blunder Areas

  • To find the area of a trapezoid, correctly identify its bases and height first.
  •  Note that the height of a trapezoid is perpendicular to both bases.