Area of a Deltoid: Applying the formula

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Question 1

Look at the deltoid in the figure:

777444

What is its area?

Question 2

Look at the deltoid in the figure:

555666

What is its area?

Question 3

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

666101010AAACCCBBBDDD

Question 4

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

AD = 12

CB = 16

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

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

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 #2

Look at the deltoid in the figure:

555666

What is its area?

Video Solution

Step-by-Step Solution

To solve the exercise, we 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 plug the data from the question into the formula:

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

Answer

15

Exercise #3

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 #4

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

AD = 12

CB = 16

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

Let's substitute the known data into the formula:

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

And that's the solution!

Answer

96 cm²

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

666444AAABBBCCCDDD

Question 2

Given the deltoid ABCD

Find the area

777555AAABBBCCCDDD

Question 3

Given the deltoid ABCD

Find the area

999666AAADDDCCCBBB

Question 4

Given the deltoid ABCD

Find the area

101010777CCCBBBAAADDD

Question 5

Given the deltoid ABCD

Find the area

999888AAADDDCCCBBB

Exercise #6

Given the deltoid ABCD

Find the area

666444AAABBBCCCDDD

Video Solution

Answer

12 12 cm².

Exercise #7

Given the deltoid ABCD

Find the area

777555AAABBBCCCDDD

Video Solution

Answer

17.5 17.5 cm².

Exercise #8

Given the deltoid ABCD

Find the area

999666AAADDDCCCBBB

Video Solution

Answer

27 27 cm².

Exercise #9

Given the deltoid ABCD

Find the area

101010777CCCBBBAAADDD

Video Solution

Answer

35 35 cm².

Exercise #10

Given the deltoid ABCD

Find the area

999888AAADDDCCCBBB

Video Solution

Answer

36 36 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

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

Question 3

Given the deltoid ABCD

Find the area

888111111AAADDDCCCBBB

Question 4

Given the deltoid ABCD

Find the area

555999AAADDDCCCBBB

Question 5

Given the deltoid ABCD

Find the area

555888AAADDDCCCBBB

Exercise #11

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 #12

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

Exercise #13

Given the deltoid ABCD

Find the area

888111111AAADDDCCCBBB

Video Solution

Answer

44 44 cm².

Exercise #14

Given the deltoid ABCD

Find the area

555999AAADDDCCCBBB

Video Solution

Answer

22.5 22.5 cm².

Exercise #15

Given the deltoid ABCD

Find the area

555888AAADDDCCCBBB

Video Solution

Answer

20 20 cm².

Question 1

Given the deltoid ABCD

Find the area

999151515AAADDDCCCBBB

Question 2

Given the deltoid ABCD

Find the area

13131317.517.517.5AAADDDCCCBBB

Question 3

Look at the deltoid ABCD below.

Given in cm:

AC = 7

DB = 5

Calculate the area of the deltoid.

777555AAABBBCCCDDD

Exercise #16

Given the deltoid ABCD

Find the area

999151515AAADDDCCCBBB

Video Solution

Answer

67.5 67.5 cm².

Exercise #17

Given the deltoid ABCD

Find the area

13131317.517.517.5AAADDDCCCBBB

Video Solution

Answer

113.75 113.75 cm².

Exercise #18

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.