Diagonals: Calculation using the diagonal

Calculation of the diagonal using propertiesUsing additional geometric shapesUsing Pythagoras' theorem
Question 1

AAABBBCCCDDD2524Calculate the perimeter of the rectangle ABCD.

Question 2

ABCD is a rectangle.

AC = 13

AB = 12

Calculate the length of the side BC.

Question 3

Below is the rectangle ABCD.

O is the intersection point of the diagonals of the rectangle.

AD = 8

BO = 8.5

Calculate the area of the triangle ABD.

AAABBBCCCDDDOOO8.58

Question 4

Look at the following rectangle:

AAABBBCCCDDD158

Calculate the perimeter of the triangle ABD.

Question 5

Look at the following rectangle:

AAABBBCCCDDD54

DC = 4

AC = 5

Calculate the area of the rectangle ABCD.

Examples with solutions for Diagonals: Calculation using the diagonal

Exercise #1

AAABBBCCCDDD2524Calculate the perimeter of the rectangle ABCD.

Video Solution

Step-by-Step Solution

Let's focus on triangle BCD in order to find side BC.

We'll use the Pythagorean theorem using our values:

BC2+DC2=BD2 BC^2+DC^2=BD^2

BC2+242=252 BC^2+24^2=25^2

BC2=625−576=49 BC^2=625-576=49

Let's now remove the square root:

BC=7 BC=7

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

DC=AB=24 DC=AB=24

BC=AD=7 BC=AD=7

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

24+7+24+7=14+48=62 24+7+24+7=14+48=62

Answer

62

Exercise #2

ABCD is a rectangle.

AC = 13

AB = 12

Calculate the length of the side BC.

Video Solution

Step-by-Step Solution

When writing the name of a polygon, the letters will always be in the order of the sides:

This is a rectangle ABCD:

This is a rectangle ABDC:

Always go in order, and always with the right corner to the one we just mentioned.

Answer

5

Exercise #3

Below is the rectangle ABCD.

O is the intersection point of the diagonals of the rectangle.

AD = 8

BO = 8.5

Calculate the area of the triangle ABD.

AAABBBCCCDDDOOO8.58

Video Solution

Step-by-Step Solution

According to the given information, we can claim that:

BD=2BO=8.5×2=17 BD=2BO=8.5\times2=17

Now let's look at triangle ABD to calculate side AB

AB2+AD2=BD2 AB^2+AD^2=BD^2

Let's input the known data:

AB2+82=172 AB^2+8^2=17^2

AB2=289−64=225 AB^2=289-64=225

We'll take the square root

AB=15 AB=15

Now let's calculate the area of triangle ABD:

15×82=1202=60 \frac{15\times8}{2}=\frac{120}{2}=60

Answer

60

Exercise #4

Look at the following rectangle:

AAABBBCCCDDD158

Calculate the perimeter of the triangle ABD.

Video Solution

Answer

40

Exercise #5

Look at the following rectangle:

AAABBBCCCDDD54

DC = 4

AC = 5

Calculate the area of the rectangle ABCD.

Video Solution

Answer

12

Question 1

Look at the following rectangle:

AAABBBCCCDDD1213

Calculate the area of the triangle ABC.

Question 2

Given the rectangle such that:

O is the intersection point of the diagonals of the rectangle.

Given: AD=6 , AB=8

Calculate the length of the section BO.

AAABBBCCCDDDOOO86

Question 3

Given the rectangle ABCD when

O is the intersection point of the diagonals of the rectangle.

Given: BC=5 , BO=6.5

Calculate the length of the section AB.

AAABBBCCCDDDOOO6.55

Question 4

Below is the rectangle ABCD.

O is the intersection point of the diagonals of the rectangle.

DC = 15

OC = 8.5

Calculate the area of the rectangle ABCD.

AAABBBCCCDDDOOO8.515

Exercise #6

Look at the following rectangle:

AAABBBCCCDDD1213

Calculate the area of the triangle ABC.

Video Solution

Answer

30

Exercise #7

Given the rectangle such that:

O is the intersection point of the diagonals of the rectangle.

Given: AD=6 , AB=8

Calculate the length of the section BO.

AAABBBCCCDDDOOO86

Video Solution

Answer

5

Exercise #8

Given the rectangle ABCD when

O is the intersection point of the diagonals of the rectangle.

Given: BC=5 , BO=6.5

Calculate the length of the section AB.

AAABBBCCCDDDOOO6.55

Video Solution

Answer

12

Exercise #9

Below is the rectangle ABCD.

O is the intersection point of the diagonals of the rectangle.

DC = 15

OC = 8.5

Calculate the area of the rectangle ABCD.

AAABBBCCCDDDOOO8.515

Video Solution

Answer

120

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