Area of a Kite Practice Problems and Solutions Online

Master kite area calculations with step-by-step practice problems. Learn convex and concave deltoid formulas, diagonal properties, and solve real geometry exercises.

📚Master Kite Area Calculations with Interactive Practice
  • Calculate kite area using diagonal multiplication formula A = (d₁ × d₂)/2
  • Identify and work with convex and concave deltoid properties
  • Apply diagonal bisector properties to solve reverse calculation problems
  • Distinguish between main and secondary diagonals in kite geometry
  • Solve multi-step problems involving kite area and diagonal lengths
  • Practice with real exam-style quadrilateral geometry questions

Understanding Area of a Deltoid

Complete explanation with examples

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}

A8 - Area formula of the kite

Detailed explanation

Practice Area of a Deltoid

Test your knowledge with 28 quizzes

Given the deltoid ABCD

Find the area

555161616AAADDDCCCBBB

Examples with solutions for Area of a Deltoid

Step-by-step solutions included
Exercise #1

Look at the deltoid in the figure:

777444

What is its area?

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

Video Solution
Exercise #2

Look at the deltoid in the figure:

555666

What is its area?

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

Video Solution
Exercise #3

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

666101010AAACCCBBBDDD

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

Video Solution
Exercise #4

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

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

Video Solution
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

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:

 8DB2=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

Video Solution

Frequently Asked Questions

What is the formula for calculating the area of a kite?

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The area of a kite is calculated using the formula A = (d₁ × d₂)/2, where d₁ and d₂ are the lengths of the two diagonals. Simply multiply the diagonal lengths and divide by 2.

What's the difference between a convex and concave kite?

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A convex kite has both diagonals inside the shape and crossing each other. A concave kite has one diagonal (main) inside and the other diagonal (secondary) extending outside the kite shape.

How do kite diagonals relate to each other?

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Kite diagonals are always perpendicular to each other. The main diagonal acts as a perpendicular bisector of the secondary diagonal, dividing it into two equal parts.

Can I find diagonal length if I know the kite's area?

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Yes, use reverse calculation with the area formula. If you know the area and one diagonal length, solve A = (d₁ × d₂)/2 for the unknown diagonal by rearranging to d₂ = 2A/d₁.

What are the key properties of a kite I need to remember?

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Remember these properties: 1) Two pairs of adjacent sides are equal, 2) Diagonals are perpendicular, 3) Main diagonal bisects the secondary diagonal, 4) Angles between equal adjacent sides are equal.

Is a rhombus a special type of kite?

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Yes, a rhombus is a special case of a kite where all four sides are equal length. A square is also a special kite where all sides and angles are equal.

How do I solve kite area problems step by step?

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Follow these steps: 1) Identify the diagonal lengths, 2) Apply the formula A = (d₁ × d₂)/2, 3) For reverse problems, rearrange the formula to solve for unknowns, 4) Use kite properties like diagonal bisection when needed.

What math topics should I know before studying kite area?

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You should understand basic multiplication and division, perpendicular lines, triangles (especially isosceles), and basic quadrilateral properties. Knowledge of coordinate geometry can also be helpful.

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