Trapezoid - Regular or Isosceles

Definition: A regular trapezoid is a trapezoid whose non-parallel sides are congruent (of equal length).

Interactivity 1: Regular trapezoid Directions for interactivity

Click and drag the slider buttons to change the size. Click and drag point B to move and point А to rotate.

Basic formulas for a regular trapezoid with base a , top b и height h are:

area: A=\,\frac{a+b}{2} \, h (same as for any trapezoid)
c=\sqrt{ \left( \frac{a-b}{2} \right)^2+h^2} length of the non-parallel sides c (using Pythagoras') , a h=\sqrt{ c^2-\left( \frac{a-b}{2} \right)^2}
perimeter: L=a+b+2c

Examples for the area and perimeter of a regular trapezoid.

Check the following examples using the above interactivity.

Dimensions of the trapezoid:			Area	Side	Perimeter
a	b	h	A=\frac{a+b}{2} \, h	c=\sqrt{ \left( \frac{a-b}{2} \right)^2+h^2}	L=a+b+2c
10 \,cm	4 \,cm	2 \,cm	\frac{10+4}{2} \,cm \cdot 3 \,cm=14 \,cm^2	c=\sqrt{ \left( \frac{10-4}{2} \right)^2+2^2} \,= 3,6 \,cm	L=21,2 \,cm
8 \,mm	5 \,mm	2 \,mm	\frac{8+5}{2} \,mm \cdot 2 \,mm=13 \,mm^2	c=\sqrt{ \left( \frac{8-5}{2} \right)^2+2^2} \,= 2,5 \,mm	L= 18 \,mm
0,09 \,m	8 \,cm	30 \,mm	\frac{9+8}{2} \,cm \cdot 3 \,cm=25,5 \,cm^2	c=\sqrt{ \left( \frac{9-8}{2} \right)^2+3^2} \,= 3 \,cm	L= 23,1 \,cm

Interactivity 2: Construct a regular trapezoid

1. Examine the regular trapezoid in the above interactivity.. 2. Now construct a regular trapezoid with the same properties. If you need help with the steps, click here to open a new window with directions ?. Check whether your construction is stable - Is your construction always a regular trapezoid no matter what slider or point you move?

Rules

The diagonals of a regular trapezoid are congruent (same length).

Click and drag points A and B.

Notice the difference between these and the rules of trapezoids!

Related themes:

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navy

Page last modified on October 10, 2008, at 12:48 AM