Trapezoid Symbols

In geometry, a trapezoid is a four-sided figure with one pair of parallel sides. A trapezoid is denoted as  ABCD with vertices ABCD. In this article we shall discuss about the area and properties of trapezoid symbols. A trapezoid  has only one pair of sides parallel and hence it not a parallelogram.

Trapezoid Symbols

Area of trapezoid = 1  h (a + b)
2

Properties of Trapezoid Symbols:


1) Here a & b are the length of parallel sides and h is the height

2) An isosceles trapezoid  has the base angle having similar measure.

3) The other pair opposite sides of AD and BC have the same length

4) The diagonal cut each other in mutually similar ratio

5) The line meeting the mid points of parallel sides bisects each other.



Example Problems:

Example 1:   Find all other angles in an isosceles trapezoid ABCD.



We know that, m
54⁰+ m
m
As we know, the base angles of an isosceles trapezoid are congruent.

Hence m
Example 2:  Evaluate the area of the trapezoid, the perpendicular distance is 10 cm and parallel sides are 2cm and 8 cm.

Solution:

Given:    a = 2 cm , b = 8 cm, h = 10cm.

Area of the trapezoid is given by,

A  =  1 (a + b) x h sq.units
2

A  = 1 x (2 + 8) x 10
2

= 1 x 10 x 10
2

= 100
2

=50

Area of trapezium = 50 square centimeter.

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Practice problems:

Problem 1:  Find all other angles in an isosceles trapezoid ABCD.



Solution: m
Problem 2: Evaluate the area of the trapezoid, the perpendicular distance is 12 cm and parallel sides are 10cm and 2 cm.

Solution: Area of trapezium = 72 square centimeter.