Deltoid - Examples, Exercises and Solutions

Let's begin by reminding ourselves of the formula for the area of a kite

$\frac{Diagonal1\times Diagonal2}{2}$

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

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

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!

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!

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:

 $\frac{8\cdot DB}{2}=32$

We reduce the 8 and the 2:

$4DB=32$

Divide by 4

$DB=8$

To solve the problem, we need to remember the formula for the area of a rhombus:

The product of the diagonals multiplied together and divided by 2.

Let's plug in the data we have into the formula:

(8*X)=60
2

Note that we can simplify the fraction, thus eliminating the denominator:

4X=60

Let's divide the equation by 4

X=15

We substitute the data we have into the formula for the area of the kite:

$S=\frac{AC\times BD}{2}$

$42=\frac{AC\times14}{2}$

We multiply by 2 to remove the denominator:

 $14AC=84$

Then divide by 14:

$AC=6$

In a rhombus, the main diagonal crosses the second diagonal, therefore:

$AO=\frac{AC}{2}=\frac{6}{2}=3$

To solve the question, we first need to remember the formula for the area of a kite:

Diagonal * Diagonal / 2

This means that if we substitute the given data we can see that:

a(2a+2)/2 = area of the kite

Let's remember that we are also given the area, so we'll put that in the equation too

a(2a+2)/2 = 6a

Now we have an equation that we can easily solve.

First, let's get rid of the fraction, so we'll multiply both sides of the equation by 2

a(2a+2)=6a*2
a(2a+2)=12a

Let's expand the parentheses on the left side of the equation

2a²+2a=12a

2a²=10a

Let's divide both sides of the equation by a

2a=10

Let's divide again by 2

a=5

And that's the solution!

We can calculate the area of rectangle ABCD:

$20\times30=600$

Let's divide the deltoid along its length and width and add the following points:

Now we can calculate the area of deltoid PMNK:

$PMNK=\frac{PN\times MK}{2}=\frac{20\times30}{2}=\frac{600}{2}=300$