Area of a Deltoid: Applying 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 shapesFinding Area based off Perimeter and Vice VersaCalculate The Missing Side based on the formula
Question 1

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

Question 2

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

666101010AAACCCBBBDDD

Question 3

Look at the deltoid in the figure:

555666

What is its area?

Question 4

Look at the deltoid in the figure:

777444

What is its area?

Question 5

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

S=32S=32S=32888AAABBBCCCDDD

Examples with solutions for Area of a Deltoid: Applying the formula

Exercise #1

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

Video Solution

Step-by-Step Solution

First, let's recall the formula for the area of a rhombus:

(Diagonal 1 * Diagonal 2) divided by 2

Now we will substitute the known data into the formula, giving us the answer:

(12*16)/2
192/2=
96

Answer

96 cm²

Exercise #2

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

666101010AAACCCBBBDDD

Video Solution

Step-by-Step Solution

To solve the exercise, we first need to remember how to calculate the area of a rhombus:

(diagonal * diagonal) divided by 2

Let's plug in the data we have from the question

10*6=60

60/2=30

And that's the solution!

Answer

30

Exercise #3

Look at the deltoid in the figure:

555666

What is its area?

Video Solution

Step-by-Step Solution

To solve the exercise, we first need to know the formula for calculating the area of a kite:

It's also important to know that a concave kite, like the one in the question, has one of its diagonals outside the shape, but it's still its diagonal.

Let's now substitute the data from the question into the formula:

(6*5)/2=
30/2=
15

Answer

15

Exercise #4

Look at the deltoid in the figure:

777444

What is its area?

Video Solution

Step-by-Step Solution

Let's begin by reminding ourselves of the formula for the area of a kite

Diagonal1×Diagonal22 \frac{Diagonal1\times Diagonal2}{2}

Both these values are given to us in the figure thus we can insert them directly into the formula:

(4*7)/2

28/2

14

Answer

14

Exercise #5

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

S=32S=32S=32888AAABBBCCCDDD

Video Solution

Step-by-Step Solution

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide the product by 2.

We substitute the known data into the formula:

 8⋅DB2=32 \frac{8\cdot DB}{2}=32

We reduce the 8 and the 2:

4DB=32 4DB=32

Divide by 4

DB=8 DB=8

Answer

8 cm

Question 1

Given the deltoid ABCD

Find the area

101010777CCCBBBAAADDD

Question 2

Given the deltoid ABCD

Find the area

999666AAADDDCCCBBB

Question 3

Given the deltoid ABCD

Find the area

999888AAADDDCCCBBB

Question 4

Given the deltoid ABCD

Find the area

666444AAABBBCCCDDD

Question 5

Given the deltoid ABCD

Find the area

777555AAABBBCCCDDD

Exercise #6

Given the deltoid ABCD

Find the area

101010777CCCBBBAAADDD

Video Solution

Answer

35 35 cm².

Exercise #7

Given the deltoid ABCD

Find the area

999666AAADDDCCCBBB

Video Solution

Answer

27 27 cm².

Exercise #8

Given the deltoid ABCD

Find the area

999888AAADDDCCCBBB

Video Solution

Answer

36 36 cm².

Exercise #9

Given the deltoid ABCD

Find the area

666444AAABBBCCCDDD

Video Solution

Answer

12 12 cm².

Exercise #10

Given the deltoid ABCD

Find the area

777555AAABBBCCCDDD

Video Solution

Answer

17.5 17.5 cm².

Question 1

Given the deltoid ABCD

Find the area

13131317.517.517.5AAADDDCCCBBB

Question 2

Given the deltoid ABCD

Find the area

555888AAADDDCCCBBB

Question 3

Given the deltoid ABCD

Find the area

555999AAADDDCCCBBB

Question 4

Given the deltoid ABCD

Find the area

888111111AAADDDCCCBBB

Question 5

Given the deltoid ABCD

Find the area

999151515AAADDDCCCBBB

Exercise #11

Given the deltoid ABCD

Find the area

13131317.517.517.5AAADDDCCCBBB

Video Solution

Answer

113.75 113.75 cm².

Exercise #12

Given the deltoid ABCD

Find the area

555888AAADDDCCCBBB

Video Solution

Answer

20 20 cm².

Exercise #13

Given the deltoid ABCD

Find the area

555999AAADDDCCCBBB

Video Solution

Answer

22.5 22.5 cm².

Exercise #14

Given the deltoid ABCD

Find the area

888111111AAADDDCCCBBB

Video Solution

Answer

44 44 cm².

Exercise #15

Given the deltoid ABCD

Find the area

999151515AAADDDCCCBBB

Video Solution

Answer

67.5 67.5 cm².

Question 1

Look at the deltoid ABCD below.

Diagonal DB = 4

The area of the deltoid is 24 cm².

Calculate the diagonal AC.

S=24S=24S=24444AAABBBCCCDDD

Question 2

Look at the deltoid ABCD below.

Given in cm:

AC = 7

DB = 5

Calculate the area of the deltoid.

777555AAABBBCCCDDD

Question 3

Shown below is the deltoid ABCD.

The diagonal AC is 3 cm long.

The area of the deltoid is 18 cm².

Calculate the diagonal DB.

S=18S=18S=18333AAABBBCCCDDD

Exercise #16

Look at the deltoid ABCD below.

Diagonal DB = 4

The area of the deltoid is 24 cm².

Calculate the diagonal AC.

S=24S=24S=24444AAABBBCCCDDD

Video Solution

Answer

12 cm

Exercise #17

Look at the deltoid ABCD below.

Given in cm:

AC = 7

DB = 5

Calculate the area of the deltoid.

777555AAABBBCCCDDD

Video Solution

Answer

17.5 cm².

Exercise #18

Shown below is the deltoid ABCD.

The diagonal AC is 3 cm long.

The area of the deltoid is 18 cm².

Calculate the diagonal DB.

S=18S=18S=18333AAABBBCCCDDD

Video Solution

Answer

12 cm