Perimeter of a Rectangle: Comprehension exercises

Look at the following rectangle:

Find its perimeter.

Since in a rectangle all pairs of opposite sides are equal:

$AD=BC=5$

$AB=CD=9$

Now we calculate the perimeter of the rectangle by adding the sides:

$5+5+9+9=10+18=28$

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Look at the rectangle below:

Calculate its perimeter.

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

$AB=CD=10$

$BC=AD=7$

Now let's add all the sides together to find the perimeter of the rectangle:

$10+7+10+7=20+14=34$

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What is the perimeter of the given rectangle ABCD?

In the statement, we have two rectangles that are connected by a common side,

The left quadrilateral, AEFD, has a known side - AD

The right quadrilateral, EBCF, also has only one known side: FC

In the question, we are asked for the perimeter of the rectangle ABCD,

For this, we need its sides, and since the opposite sides in a rectangle are equal, we need at least two adjacent sides.

We are given the side AD, but the side DC is only partially given.

We have no way of finding the missing part: DF, so we have no way of answering the question.

This is the solution!

It is not possible to know

ABCD, EFCD, and ABFE are all rectangles.

Calculate the perimeter of rectangle ABCD.

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

$AE=BF=5$

$AB=CD=9$

Now we can calculate side BC:

$5+3=8$

Since side BC is equal to side AD, it is also equal to 8

Let's calculate the perimeter of rectangle ABCD:

$9+8+9+8=18+16=34$

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Given the following rectangle:

What is the perimeter of the rectangle ABCD?

Based on the given data, we know that:

$AD=BC=5$

$AB=AE+EB$

$AB=7+EB$

We are missing data to determine the length of AB, and therefore we cannot calculate the perimeter of the rectangle

It is not possible to know

ABCD and EBFC are rectangles.

Calculate the perimeter of the rectangle ABCD.

Since in a rhombus every pair of opposite sides are equal to each other, we can claim that:

$EF=BC=AD=5$

$FC=EB=3$

To calculate side AB, we will use the following formula:

$AB=AE+EB$

Since we are only given the length of EB, we don't have enough information and cannot calculate the lengths of the other sides.

Not enough data

ABCD and EBFC are rectangles.

Calculate the perimeter of rectangle ABCD.

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

$EF=BC=AD=5$

$FC=EB=3$

Now we can calculate side AB:

$8+3=11$

Since AB and CD are equal to each other, side CD is also equal to 11

Let's calculate the perimeter of the rectangle:

$11+5+11+5=22+10=32$

32

Look at the following rectangle:

What is the perimeter of the rectangle EFCD?

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

$BC=AD=5$

Now we can calculate side ED:

$AD-AE=ED$

Let's substitute the known data:

$5-3=ED$

$ED=2$

Side ED is equal to side FC and therefore it is also equal to 2

We can also claim that:

$AB=CD=EF=7$

Now we can calculate the perimeter of rectangle EFCD:

$2+7+2+7=4+14=18$

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What is the perimeter of the given rectangle ABCD?

Given that in the smaller rectangle ED=CF=4 (each pair of opposite sides in the rectangle are equal)

We can therefore calculate for the rectangle ABCD that BC=6+4=10

Now we can state in the rectangle ABCD that BC=AD=10

Next we calculate the perimeter of the rectangle by adding together all of the sides:

DC=AB=15

Hence the perimeter of the rectangle ABCD is equal to:

$10+10+15+15=20+30=50$

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Rectangle ABCD contains three other rectangles inside it.

Calculate the perimeter of ABCD.

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

$GH=AE=DF=9$

Now we can calculate side CD:

$9+5=14$

Since side CD is equal to side AB, it is also equal to 14

$BC=AD=7$

Let's calculate the perimeter of rectangle ABCD:

$7+14+7+14=14+28=42$

42

Rectangle ABCD contains three other rectangles.

Calculate the perimeter of ABCD.

Let's look at rectangle EBHF where we are given:

EF=BH=5

FH=EB=6

From this we can calculate AB:

7+6=13

Now we have a pair of sides in rectangle ABCD:

AB=DC=13

We know that EF=BH=AG=5

We therefore do not have enough additional data to calculate the sides AD and BC.

Not enough data

Given the following rectangle:

What is the perimeter of the rectangle ABCD?

According to the given data:

$JC=HB=3$

$DI=AG=3$

$FD=EC=3$

$BE=AF=4$

$GH=JI=6$

Now we can calculate sides AB and DC

$3+6+3=9+3=12$

And also sides AD and BC

$4+3=7$

Now we can calculate the perimeter of rectangle ABCD:

$12+7+12+7=24+14=38$

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What is the perimeter of the given rectangle ABCD?

According to the data let's consider:

$CF=DE=3$

$AE=BF=5$

Now we can calculate BC:

$5+3=8$

$AD=BC=8$

Next we pay attention to any additional information and it seems that:

$GB=HC=4$

$DH=AG=7$

Hence we can calculate AB:

$7+4=11$

$AB=DC=11$

Lastly we can calculate the perimeter of the rectangle ABCD:

$8+8+11+11=$

$16+22=38$

38

Look at the following rectangle:

What is the perimeter of the rectangle ABFE?

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:

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

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Look at the following rectangle:

ΔEDC is equilateral.

Calculate the perimeter of the rectangle.

A rectangle has two pairs of equal opposite sides.

That is:

BC=AD=4

AB=DC

In an equilateral triangle, all sides are equal, therefore:
EC=CD=DE

We know that EC=8, so:

EC=CD=DE=8

We know that:

AB=DC

Therefore:

AB=DC=8

Remember that the perimeter of a rectangle is equal to the sum of all its sides, therefore:

AB+BC+DC+AD

We substitute in all its known sides:

8+4+8+4=

24

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ABCD is a rectangle.

AIFE and EFHG are also rectangles.

Calculate the perimeter of the rectangle ABCD.

Not enough data

Below is a figure composed of three rectangles:

Calculate the perimeter of rectangle ABCF.

26

Given rectangle ABCD.

AIFE rectangle, EFHG rectangle.

Find the perimeter of rectangle ABCD.

32

The figure below is composed of three rectangles:

Calculate the perimeter of rectangle ABDE.

36

Rectangle ABCD contains three other rectangles inside of it.

Calculate the perimeter of rectangle ABCD.

42