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?

00:00 Calculate the perimeter of rectangle ABFE

00:08 Opposite sides are equal in rectangle GBHC

00:21 Opposite sides are equal in rectangle EDFC

00:32 Segment (BE) equals the entire side (BC) minus segment (FC)

00:40 Opposite sides are equal in rectangle ABEF

00:48 The entire side equals the sum of its parts

00:55 Opposite sides are equal in rectangle ABCD

01:05 The perimeter of the rectangle equals the sum of its sides

01:17 Let's substitute appropriate values and solve for the perimeter

01:44 And this is the solution to the 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:

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