Area of a Deltoid: Using Pythagoras' theorem

Applying the formulaCalculate The Missing Side based on the formulaCalculation using percentagesFinding Area based off Perimeter and Vice VersaIdentifying and defining elementsSubtraction or addition to a larger shapeUsing additional geometric shapesUsing external heightUsing ratios for calculationUsing variablesVerifying whether or not the formula is applicable
Question 1

ABCD is a kite.

BD is the diagonal of a square that has an area equal to 36 cm².

\( AC=2x \)

Express the area of the kite in terms of X.

AAABBBCCCDDD

Question 2

Look at the deltoid ABCD shown below.

AO = 4

OB = 3

The perimeter of the deltoid is equal to 28 cm.

Calculate the area of the deltoid ABCD.

444333AAABBBCCCDDDOOO

Question 3

The deltoid ABCD is shown below.

Given in cm:

AO = 4

OB = 3

P = 28

Calculate the area of the deltoid.

444333AAABBBCCCDDDOOO

Question 4

Given ABCD deltoid AB=AC DC=BD

The diagonals of the deltoid intersect at the point O

Given in cm AO=12 OD=4

The area of the deltoid is equal to 48 cm².

Calculate the side CD

S=48S=48S=48121212444CCCAAABBBDDDOOO

Question 5

The perimeter of the deltoid ABCD shown below is 30 cm².

Calculate its area.

333444AAABBBCCCDDDEEE

Examples with solutions for Area of a Deltoid: Using Pythagoras' theorem

Exercise #1

ABCD is a kite.

BD is the diagonal of a square that has an area equal to 36 cm².

AC=2x AC=2x

Express the area of the kite in terms of X.

AAABBBCCCDDD

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Calculate the side length of the square using the given area.
  • Step 2: Determine the length of BDBD using the side length.
  • Step 3: Use the kite area formula with diagonals BDBD and AC=2xAC=2x.

Now, let's work through each step:

Step 1: The area of the square is 36 cm². The side length of the square, denoted as ss, can be calculated by taking the square root of the area:

s=36=6 cms = \sqrt{36} = 6 \text{ cm}

Step 2: To find diagonal BDBD, we use the relationship for the diagonal of a square in terms of its side:

BD=s2BD = s \sqrt{2}. Given s=6s = 6, we compute:

BD=62 cmBD = 6\sqrt{2} \text{ cm}

Step 3: Now, we apply the formula for the area of a kite, which is 12×d1×d2\frac{1}{2} \times d1 \times d2, where d1=BD=62d1 = BD = 6\sqrt{2} and d2=AC=2xd2 = AC = 2x:

The area AA of the kite is:

A=12×62×2x=62x cm2A = \frac{1}{2} \times 6\sqrt{2} \times 2x = 6\sqrt{2}x \text{ cm}^2

Therefore, the area of the kite in terms of xx is 62x6\sqrt{2}x cm².

Answer

62x 6\sqrt{2}x cm²

Exercise #2

Look at the deltoid ABCD shown below.

AO = 4

OB = 3

The perimeter of the deltoid is equal to 28 cm.

Calculate the area of the deltoid ABCD.

444333AAABBBCCCDDDOOO

Video Solution

Answer

37.5 cm².

Exercise #3

The deltoid ABCD is shown below.

Given in cm:

AO = 4

OB = 3

P = 28

Calculate the area of the deltoid.

444333AAABBBCCCDDDOOO

Video Solution

Answer

37.5 cm²

Exercise #4

Given ABCD deltoid AB=AC DC=BD

The diagonals of the deltoid intersect at the point O

Given in cm AO=12 OD=4

The area of the deltoid is equal to 48 cm².

Calculate the side CD

S=48S=48S=48121212444CCCAAABBBDDDOOO

Video Solution

Answer

5 cm

Exercise #5

The perimeter of the deltoid ABCD shown below is 30 cm².

Calculate its area.

333444AAABBBCCCDDDEEE

Video Solution

Answer

391 3\sqrt{91} cm²

Question 1

The area of a concave deltoid is 9 cm².
What is the value of X?

\( \)555333XXX

Question 2

ABCD is a kite

ABED is a trapezoid with an area of 22 cm².

AC is 6 cm long.

Calculate the area of the kite.

444444555666AAABBBDDDCCCEEE

Question 3

Given ABCD deltoid AB=BC DA=DC

The diagonals of the deltoid intersect at the point O

Given in cm BO=7 OC=4 AD=5

Calculate the area of the deltoid

555444777AAABBBCCCDDDOOO

Question 4

The deltoid ABCD has an area equal to 90 cm².

If the area of the triangle BCD is equal to 18 cm², then what is the perimeter of the deltoid?

999AAABBBCCCDDDEEE

Question 5

The perimeter of deltoid ABCD is equal to 20 cm.


\( AC=\sqrt{41}-1 \)

Calculate the area of the deltoid.

333AAABBBCCCDDD

Exercise #6

The area of a concave deltoid is 9 cm².
What is the value of X?

555333XXX

Video Solution

Answer

1 cm

Exercise #7

ABCD is a kite

ABED is a trapezoid with an area of 22 cm².

AC is 6 cm long.

Calculate the area of the kite.

444444555666AAABBBDDDCCCEEE

Video Solution

Answer

613 6\sqrt{13} cm²

Exercise #8

Given ABCD deltoid AB=BC DA=DC

The diagonals of the deltoid intersect at the point O

Given in cm BO=7 OC=4 AD=5

Calculate the area of the deltoid

555444777AAABBBCCCDDDOOO

Video Solution

Answer

40 cm²

Exercise #9

The deltoid ABCD has an area equal to 90 cm².

If the area of the triangle BCD is equal to 18 cm², then what is the perimeter of the deltoid?

999AAABBBCCCDDDEEE

Video Solution

Answer

30+285 30+2\sqrt{85}

Exercise #10

The perimeter of deltoid ABCD is equal to 20 cm.


AC=41−1 AC=\sqrt{41}-1

Calculate the area of the deltoid.

333AAABBBCCCDDD

Video Solution

Answer

328 \sqrt{328} cm²

Question 1

The perimeter of the deltoid ABCD is equal to \( 5x \).

\( BD=4 \)

Express the area of the deltoid in terms of X.

AAABBBCCCDDD

Exercise #11

The perimeter of the deltoid ABCD is equal to 5x 5x .

BD=4 BD=4

Express the area of the deltoid in terms of X.

AAABBBCCCDDD

Video Solution

Answer

2x2−4+22.25x2−4 2\sqrt{x^2-4}+2\sqrt{2.25x^2-4} cm²