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

Exercise #1

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 #2

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 #3

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 #4

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

555333XXX

Video Solution

Answer

1 cm

Exercise #5

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 #6

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

Answer

62x 6\sqrt{2}x cm²