Perimeter of a Trapezoid: Comparison between 2 of the same shape with an identical perimeter

Examples with solutions for Perimeter of a Trapezoid: Comparison between 2 of the same shape with an identical perimeter

Exercise #1

What can be said about the two trapezoids in the diagram?

x+517y10x12

Video Solution

Step-by-Step Solution

We calculate the perimeter of the left trapezoid:

P=10+12+x+y P=10+12+x+y

P=22+x+y P=22+x+y

We calculate the perimeterof the right trapezoid:

P=x+5+17+y3+2y3 P=x+5+17+\frac{y}{3}+\frac{2y}{3}

P=x+22+2y+y3 P=x+22+\frac{2y+y}{3}

P=x+22+3y3 P=x+22+\frac{3y}{3}

P=x+22+y P=x+22+y

It can be seen that the two perimeters are identical to each other.

Answer

Their perimeters are identical.

Exercise #2

Given the trapezoids in the drawing.

Are they the same trapezoid?

CCCxx+1610677

Video Solution

Step-by-Step Solution

We calculate the perimeter of the left trapezoid:

P=6+10+7+52x+5 P=6+10+7+\frac{5}{2}x+5

P=28+52x P=28+\frac{5}{2}x

We calculate the perimeter of the right trapezoid:

P=7+x+x+16+x2+5 P=7+x+x+16+\frac{x}{2}+5

P=212x+28 P=2\frac{1}{2}x+28

P=52x+28 P=\frac{5}{2}x+28

The perimeters of the two trapezoids are equal to each other.

Answer

No, but their perimeter is identical.

Exercise #3

What is the perimeter of each trapezoid?

Are their areas equal?

43362275

Video Solution

Answer

a -16, b -16, yes.

Exercise #4

What are the perimeters of the trapezoid?

Are their areas identical?

4775BA21173

Video Solution

Answer

pA=pB=23 pA=pB=23 , not necessarily

Exercise #5

How long is B2C2 given that the perimeters of the two trapezoids are equal?

555666777XXX555777XXXA1A1A1B1B1B1D1D1D1C1C1C1A2A2A2B2B2B2C2C2C2D2D2D2

Video Solution

Answer

6

Exercise #6

Two trapezoids are shown below.

Are their perimeters the same?

x3x152x+1052x

Video Solution

Answer

Yes, equal to 412x+15 4\frac{1}{2}x+15

Exercise #7

The two trapezoids below are isosceles.

What is the size of C2D2 if the trapezoids are equal?

2X2X2X4443X3X3X4443X3X3X666666A1A1A1B1B1B1D1D1D1C1C1C1A2A2A2B2B2B2D2D2D2C2C2C2

Video Solution

Answer

2X-4

Exercise #8

Calculate X given that the perimeters of the two trapezoids are equal.

5X5X5X2X-22X-22X-26X6X6X2X+12X+12X+14X4X4X3X3X3XA1A1A1B1B1B1D1D1D1C1C1C1A2A2A2B2B2B2D2D2D2C2C2C2X-14X+1

Video Solution

Answer

5 5