Area of a Deltoid: Calculate The Missing Side based on the formula

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Question 1

The deltoid below has an area of 60 cm².

888XXX

What is the value of X?

Question 2

The kite ABCD shown below has an area of 42 cm².

AB = BC

DC = AD

BD = 14

The diagonals of the kite intersect at point 0.

Calculate the length of side AO.

S=42S=42S=42141414DDDAAABBBCCCOOO

Question 3

Given the deltoid ABCD

Side length BD equals 4 cm

The area of the deltoid is equal to 20 cm².

Find the length of the side AC

S=20S=20S=20444AAADDDCCCBBB

Question 4

Given the deltoid ABCD

Side length AC equals 10 cm

The area of the deltoid is equal to 40 cm².

Find the length of the side BD

S=40S=40S=40101010AAABBBCCCDDD

Question 5

Given the deltoid ABCD

Side length BD equals 6 cm

The area of the deltoid is equal to 54 cm².

Find the length of the side AC

S=54S=54S=54666AAABBBCCCDDD

Examples with solutions for Area of a Deltoid: Calculate The Missing Side based on the formula

Exercise #1

The deltoid below has an area of 60 cm².

888XXX

What is the value of X?

Video Solution

Step-by-Step Solution

To solve the problem, we need to remember the formula for the area of a rhombus:

The product of the diagonals multiplied together and divided by 2.

Let's plug in the data we have into the formula:

(8*X)=60
2

Note that we can simplify the fraction, thus eliminating the denominator:

4X=60

Let's divide the equation by 4

X=15

Answer

15

Exercise #2

The kite ABCD shown below has an area of 42 cm².

AB = BC

DC = AD

BD = 14

The diagonals of the kite intersect at point 0.

Calculate the length of side AO.

S=42S=42S=42141414DDDAAABBBCCCOOO

Video Solution

Step-by-Step Solution

We substitute the data we have into the formula for the area of the kite:

S=AC×BD2 S=\frac{AC\times BD}{2}

42=AC×142 42=\frac{AC\times14}{2}

We multiply by 2 to remove the denominator:

 14AC=84 14AC=84

Then divide by 14:

AC=6 AC=6

In a rhombus, the main diagonal crosses the second diagonal, therefore:

AO=AC2=62=3 AO=\frac{AC}{2}=\frac{6}{2}=3

Answer

3 cm

Exercise #3

Given the deltoid ABCD

Side length BD equals 4 cm

The area of the deltoid is equal to 20 cm².

Find the length of the side AC

S=20S=20S=20444AAADDDCCCBBB

Video Solution

Answer

10 10 cm

Exercise #4

Given the deltoid ABCD

Side length AC equals 10 cm

The area of the deltoid is equal to 40 cm².

Find the length of the side BD

S=40S=40S=40101010AAABBBCCCDDD

Video Solution

Answer

8 8 cm

Exercise #5

Given the deltoid ABCD

Side length BD equals 6 cm

The area of the deltoid is equal to 54 cm².

Find the length of the side AC

S=54S=54S=54666AAABBBCCCDDD

Video Solution

Answer

18 18 cm

Question 1

Given the deltoid ABCD

Side length AC equals 9 cm

The area of the deltoid is equal to 72 cm².

Find the length of the side BD

S=72S=72S=72999AAABBBCCCDDD

Question 2

Given the deltoid ABCD

Side length AC equals 11 cm

The area of the deltoid is equal to 44 cm².

Find the length of the side BD

S=44S=44S=44111111AAABBBCCCDDD

Question 3

Given the deltoid ABCD

Side length BD equals 7 cm

The area of the deltoid is equal to 49 cm².

Find the length of the side AC

S=49S=49S=49777AAABBBCCCDDD

Question 4

Given the deltoid ABCD

Side length AC equals 13 cm

The area of the deltoid is equal to 39 cm².

Find the length of the side BD

S=39S=39S=39131313AAABBBCCCDDD

Question 5

The deltoid ABCD is shown below.

Side length AC equals 6 cm.

The area of the deltoid is 48 cm².

What is the length of the side BD?

S=48S=48S=48666AAABBBCCCDDD

Exercise #6

Given the deltoid ABCD

Side length AC equals 9 cm

The area of the deltoid is equal to 72 cm².

Find the length of the side BD

S=72S=72S=72999AAABBBCCCDDD

Video Solution

Answer

16 16 cm

Exercise #7

Given the deltoid ABCD

Side length AC equals 11 cm

The area of the deltoid is equal to 44 cm².

Find the length of the side BD

S=44S=44S=44111111AAABBBCCCDDD

Video Solution

Answer

8 8 cm

Exercise #8

Given the deltoid ABCD

Side length BD equals 7 cm

The area of the deltoid is equal to 49 cm².

Find the length of the side AC

S=49S=49S=49777AAABBBCCCDDD

Video Solution

Answer

14 14 cm

Exercise #9

Given the deltoid ABCD

Side length AC equals 13 cm

The area of the deltoid is equal to 39 cm².

Find the length of the side BD

S=39S=39S=39131313AAABBBCCCDDD

Video Solution

Answer

6 6 cm

Exercise #10

The deltoid ABCD is shown below.

Side length AC equals 6 cm.

The area of the deltoid is 48 cm².

What is the length of the side BD?

S=48S=48S=48666AAABBBCCCDDD

Video Solution

Answer

16 16 cm

Question 1

Given the deltoid ABCD

Side length BD equals 12 cm

The area of the deltoid is equal to 60 cm².

Find the length of the side AC

S=60S=60S=60121212AAABBBCCCDDD

Question 2

Given the deltoid ABCD

Side length AC equals 8 cm

The area of the deltoid is equal to 64 cm².

Find the length of the side BD

S=64S=64S=64888AAABBBCCCDDD

Question 3

Given the deltoid ABCD

Side length AC equal to 5.5 cm

The area of the deltoid is equal to 27.5 cm².

Find the length of the side BD

S=27.5S=27.5S=27.55.55.55.5AAABBBCCCDDD

Question 4

Below is the deltoid ABCD.

Side length BD equals 15 cm.

The area of the deltoid is 60 cm².

Find the length of the side AC.

S=60S=60S=60151515AAABBBCCCDDD

Question 5

Given below is the deltoid ABCD.

Side length MD equals 3 cm.

The area of the deltoid is 72 cm².

What is the length of the side AC?

333AAABBBCCCDDDMMMS=72

Exercise #11

Given the deltoid ABCD

Side length BD equals 12 cm

The area of the deltoid is equal to 60 cm².

Find the length of the side AC

S=60S=60S=60121212AAABBBCCCDDD

Video Solution

Answer

10 10 cm

Exercise #12

Given the deltoid ABCD

Side length AC equals 8 cm

The area of the deltoid is equal to 64 cm².

Find the length of the side BD

S=64S=64S=64888AAABBBCCCDDD

Video Solution

Answer

16 16 cm

Exercise #13

Given the deltoid ABCD

Side length AC equal to 5.5 cm

The area of the deltoid is equal to 27.5 cm².

Find the length of the side BD

S=27.5S=27.5S=27.55.55.55.5AAABBBCCCDDD

Video Solution

Answer

10 10 cm

Exercise #14

Below is the deltoid ABCD.

Side length BD equals 15 cm.

The area of the deltoid is 60 cm².

Find the length of the side AC.

S=60S=60S=60151515AAABBBCCCDDD

Video Solution

Answer

8 8 cm

Exercise #15

Given below is the deltoid ABCD.

Side length MD equals 3 cm.

The area of the deltoid is 72 cm².

What is the length of the side AC?

333AAABBBCCCDDDMMMS=72

Video Solution

Answer

24 24 cm

Question 1

Shown below is the deltoid ABCD.

Side length BM equals 2 cm.

The area of the deltoid is 72 cm².

Find the length of the side AC.

AAABBBCCCDDDMMMS=72

Question 2

Given ABCD deltoid AD=AB CB=CD

The diagonals of the deltoid intersect at the point O

Given in cm AO=6 BO=5

The area of the deltoid is equal to 80 cm².

Calculate the side CO

S=80S=80S=80666555DDDAAABBBCCCOOO

Question 3

Given the deltoid ABCD

DB=4 the area of the deltoid is equal to 32 cm².

Calculate the side AC

S=32S=32S=32444AAABBBCCCDDD

Question 4

Below is the deltoid ABCD.

C = 8

The area of the deltoid is equal to 32 cm².

Calculate the side DB.

S=32S=32S=32888AAABBBCCCDDD

Question 5

Look at the deltoid ABCD below.

DB = 9

The area of the deltoid is equal to 45 cm².

Calculate the length of side AC.

S=45S=45S=45999AAABBBCCCDDD

Exercise #16

Shown below is the deltoid ABCD.

Side length BM equals 2 cm.

The area of the deltoid is 72 cm².

Find the length of the side AC.

AAABBBCCCDDDMMMS=72

Video Solution

Answer

36 36 cm

Exercise #17

Given ABCD deltoid AD=AB CB=CD

The diagonals of the deltoid intersect at the point O

Given in cm AO=6 BO=5

The area of the deltoid is equal to 80 cm².

Calculate the side CO

S=80S=80S=80666555DDDAAABBBCCCOOO

Video Solution

Answer

10

Exercise #18

Given the deltoid ABCD

DB=4 the area of the deltoid is equal to 32 cm².

Calculate the side AC

S=32S=32S=32444AAABBBCCCDDD

Video Solution

Answer

16 cm

Exercise #19

Below is the deltoid ABCD.

C = 8

The area of the deltoid is equal to 32 cm².

Calculate the side DB.

S=32S=32S=32888AAABBBCCCDDD

Video Solution

Answer

8 cm

Exercise #20

Look at the deltoid ABCD below.

DB = 9

The area of the deltoid is equal to 45 cm².

Calculate the length of side AC.

S=45S=45S=45999AAABBBCCCDDD

Video Solution

Answer

10 cm