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

Calculation using percentagesSubtraction or addition to a larger shapeVerifying whether or not the formula is applicableUsing Pythagoras' theoremUsing external heightUsing ratios for calculationIdentifying and defining elementsUsing variablesUsing additional geometric shapesApplying the formulaFinding Area based off Perimeter and Vice Versa
Question 1

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 2

The deltoid below has an area of 60 cm².

888XXX

What is the value of X?

Question 3

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 4

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

Question 5

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

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

Exercise #1

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 #2

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 #3

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 #4

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

Exercise #5

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

Question 1

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 2

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 3

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 4

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 5

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

Exercise #6

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 #7

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 #8

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 #9

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 #10

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

Question 1

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

Question 2

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 3

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 4

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 5

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

Exercise #11

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

Exercise #12

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 #13

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 #14

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 #15

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

Question 1

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

Question 2

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 3

Shown below is the deltoid ABCD.

DB = 4

The area of the deltoid is 28 cm².

Calculate the length of side AC.

S=28S=28S=28444AAABBBCCCDDD

Question 4

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 5

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

Exercise #16

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

Exercise #17

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 #18

Shown below is the deltoid ABCD.

DB = 4

The area of the deltoid is 28 cm².

Calculate the length of side AC.

S=28S=28S=28444AAABBBCCCDDD

Video Solution

Answer

14 cm²

Exercise #19

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 #20

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