Calculate Rectangle Perimeter: Finding ABFE Using 4, 5, and 10 Units

Question

Look at the following rectangle:

What is the perimeter of the rectangle ABFE?

00:04 Let's find the perimeter of rectangle A-B-F-E. Ready?

00:12 In rectangle G-B-H-C, remember! Opposite sides are the same length.

00:25 For rectangle E-D-F-C, opposite sides are equal too. That's important!

00:36 Segment B-E is the whole side B-C minus segment F-C. You got this!

00:44 Rectangle A-B-E-F also has opposite sides that are equal.

00:52 The entire side is just the sum of its parts. Simple, right?

00:59 In rectangle A-B-C-D, opposite sides are equal once more.

01:09 To find the perimeter, add up all the sides. Easy peasy!

01:21 Now, put the correct numbers into the formula and calculate the perimeter.

01:48 And there you have it! That's the solution to our problem.

Based on the given data, we can claim that:

$HC=GB=8$

$ED=FC=4$

$AE=BC=10$

Now we can calculate side AE:

$AE=10-4=6$

$AE=BF=6$

Now we can calculate side AB which is equal to side CD:

$AB=CD=EF=8+5=13$

Now we can calculate the perimeter of rectangle ABFE:

$13+6+13+6=26+12=38$