What is a Trapezoid or a Trapezium?
A special type of quadrilateral in which at least one pair of opposite sides are parallel is called a trapezoid. A trapezoid also consists of four sides, and four vertices.
Properties of a Trapezoid
- The parallel sides are called bases.
- The non-parallel sides are called legs.
- The perpendicular distance between the bases is called height or altitude.
- The two consecutive angles with a common side as the base are called base angles.
- The angles formed on the same leg, between the parallel sides, are supplementary.
- The sum of all the interior angles is 360°.
Formula for the Perimeter of a Trapezoid
The formula for the perimeter of a trapezoid = a + b + c + d
Where,
a, b, c and d are the lengths of sides of a trapezoid.
Solved Examples
Example 1: Find the perimeter of a trapezoid ABCD in which the legs measure 5 cm and 7 cm. Its bases are 15 cm and 12 cm.
Solution:
As stated in the question,
a = 5 cm
b = 7 cm
c = 15 cm
d = 12 cm
Perimeter of trapezoid = a + b + c + d
= 5 + 7 + 15 + 12
= 39 cm
So, the perimeter of the given trapezoid is 39 centimeters.
Example 2: Find the perimeter of trapezoid PQRS in with legs that measure 3 m and 4 m. Its bases measure 12 m and 5 m in length.
Solution:
As stated in the question,
a = 3 m
b = 4 m
c = 12 m
d = 5 m
Perimeter of trapezoid = a + b + c + d
= 3 + 4 + 12 + 5
= 24 m
So, the perimeter of the given trapezoid is 24 meters.
Example 3:The perimeter of trapezoid ABCD is 50 inches. The length of sides of AB = 10 in, BC = 12 in and CD = 8 in. Find the length of the side DA of the trapezoids.
Solution:
As stated in the question,
Perimeter = 50 inches
AB = 10 in
BC = 12 in
CD = 8 in
DA = ?
Perimeter of trapezoid ABCD = AB + BC + CD + DA
50 = 10 + 12 + 8 + DA
50 = 30 + DA
DA = 50 – 30 = 20 inches
So, the length of the side DA is 20 inches.
Example 4: John is observing a plot which is trapezoidal in shape. He measured the sides length of the plot and found that legs of the plot are 77 meters and 78 meters in length while the bases are 85 meters and 88 meters in length. John wants to find the length of the boundary of the trapezoidal field.
Solution:
As stated in the question,
Sides length of the trapezoidal plot,
a = 77 m
b = 78 m
c = 85 m
d = 88 m
Perimeter of the trapezoidal field = a + b + c + d
= 77 + 78 + 85 + 88
= 328 m
So, the perimeter of the trapezoidal plot is 328 meters.
A trapezoid is not a parallelogram because in a parallelogram the opposite sides are parallel to each other. However in a trapezoid only one pair of opposite sides is parallel.
Yes, a trapezoid is considered a quadrilateral because all two dimensional plane shapes that have four sides are known as quadrilaterals.
There are three types of trapezoids:
- Scalene trapezoid
- Isosceles trapezoid
- Right trapezoid
A trapezoid which contains a pair of right angles is called a right trapezoid.
A trapezoid with legs that are equal in length is called an isosceles trapezoid.
When the legs of a trapezoid are parallel to each other, which indicates that both pairs of opposite sides are parallel, the trapezoid then becomes a parallelogram.