Deltoid area - Examples, Exercises and Solutions

How do we calculate the area of a kite?

The area of the kite can be calculated by multiplying the lengths of the diagonals and dividing this product by 2 2 .

Deltoid Area Formula

To facilitate the understanding of the concept of calculus, you can use the following drawing and the accompanying formula:

A=KM×NL2A=\frac{ KM\times NL}{2}

A1 - Area of a deltoid

Practice Deltoid area

Exercise #1

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 this product by 2.

We substitute the known data into the formula:

 8DB2=32 \frac{8\cdot DB}{2}=32

We will reduce the 8 and the 2:

4DB=32 4DB=32

Divide by 4

DB=8 DB=8

Answer

8 cm

Exercise #2

Look at the deltoid in the figure:

777444

What is its area?

Video Solution

Step-by-Step Solution

Initially, let's remember the formula for the area of a kite

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

Both pieces of information already exist, so we can place them in the formula:

(4*7)/2

28/2

14

Answer

14

Exercise #3

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 #4

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

666101010AAACCCBBBDDD

Video Solution

Answer

30

Exercise #5

ABDC is a deltoid.

AB = BD

DC = CA

Given in cm:

AD = 12

CB = 16

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

Video Solution

Answer

96 cm²

Exercise #1

Look at the kite ABCD below.

Diagonal DB = 10

CB = 4

Is it possible to calculate the area of the kite? If so, what is it?

444101010AAADDDCCCBBB

Video Solution

Answer

It is not possible.

Exercise #2

Given the deltoid ABCD

Find the area

999666AAADDDCCCBBB

Video Solution

Answer

27 27 cm².

Exercise #3

Given the deltoid ABCD

Find the area

101010777CCCBBBAAADDD

Video Solution

Answer

35 35 cm².

Exercise #4

Given the deltoid ABCD

Find the area

555191919AAADDDCCCBBB

Video Solution

Answer

47.5 47.5 cm².

Exercise #5

Given the deltoid ABCD

Find the area

555888AAADDDCCCBBB

Video Solution

Answer

20 20 cm².

Exercise #1

Given the deltoid ABCD

Find the area

555161616AAADDDCCCBBB

Video Solution

Answer

40 40 cm².

Exercise #2

Given the deltoid ABCD

Find the area

999888AAADDDCCCBBB

Video Solution

Answer

36 36 cm².

Exercise #3

Given the deltoid ABCD

Find the area

555181818AAADDDCCCBBB

Video Solution

Answer

45 45 cm².

Exercise #4

Given the deltoid ABCD

Find the area

555222222AAADDDCCCBBB

Video Solution

Answer

55 55 cm².

Exercise #5

Given the deltoid ABCD

Find the area

666444AAABBBCCCDDD

Video Solution

Answer

12 12 cm².

Topics learned in later sections

  1. Area
  2. Kite