Area of a Deltoid: Using variables

Calculation using percentages Subtraction or addition to a larger shape Verifying whether or not the formula is applicable Using Pythagoras' theorem Using external height Using ratios for calculation Identifying and defining elements Using additional geometric shapes Applying the formula Finding Area based off Perimeter and Vice Versa Calculate The Missing Side based on the formula

Question 1

Given the deltoid ABCD

The main diagonal is equal to 2a+2

Secondary diagonal is equal to a

The area of the deltoid equals 6a

Calculate a a

Question 2

Below is the deltoid ABCD.

Side length BD equals 7 cm.

The area of the deltoid is equal to 98 cm².

What is the value of $a\text{?}$

Question 3

Given the deltoid ABCD

height AE formed by the diagonal extension AC

Side length ED equals 3 cm

The area of the deltoid is equal to 189 cm².

Find the value of the parameter

Question 4

Given the deltoid ABCD

Side length AC equals 7 cm

The area of the deltoid is equal to 252 cm².

Find the value of the parameter $\( a \)$

Question 5

Given the deltoid ABCD

Side length BD equals 8 cm

The area of the deltoid is equal to 180 cm².

Find the value of the parameter $\( a \)$

Examples with solutions for Area of a Deltoid: Using variables

Exercise #1

Given the deltoid ABCD

The main diagonal is equal to 2a+2

Secondary diagonal is equal to a

The area of the deltoid equals 6a

Calculate a a

Video Solution

Step-by-Step Solution

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!

Answer

5 cm

Exercise #2

Below is the deltoid ABCD.

Side length BD equals 7 cm.

The area of the deltoid is equal to 98 cm².

What is the value of $a\text{?}$

Video Solution

Answer

$4$

Exercise #3

Given the deltoid ABCD

height AE formed by the diagonal extension AC

Side length ED equals 3 cm

The area of the deltoid is equal to 189 cm².

Find the value of the parameter

Video Solution

Answer

$9$

Exercise #4

Given the deltoid ABCD

Side length AC equals 7 cm

The area of the deltoid is equal to 252 cm².

Find the value of the parameter $a$

Video Solution

Answer

$8$

Exercise #5

Given the deltoid ABCD

Side length BD equals 8 cm

The area of the deltoid is equal to 180 cm².

Find the value of the parameter $a$

Video Solution

Answer

$5$

Question 1

Look at the deltoid ABCD.

The side BD is 13 cm long.

The area of the deltoid is 182 cm².

Calculate $a\text{.}$

Question 2

Shown below is the deltoid ABCD.

Side length BD equals 5 cm.

The area of the deltoid is 45 cm².

What is the the value of $\( a? \)$

Question 3

Shown below is the deltoid ABCD.

AC = 2X

DB = X

The area of the deltoid is equal to 32 cm².

Calculate DB.

Question 4

Shown below is the deltoid ABCD.

The diagonal AC = X

Diagonal DB = 5

The area of the deltoid is 20 cm².

Calculate X.

Question 5

The deltoid ABCD is shown below.

AC = X

DB = 3X

The area of the deltoid is 27 cm².

Calculate the length of AC.

Exercise #6

Look at the deltoid ABCD.

The side BD is 13 cm long.

The area of the deltoid is 182 cm².

Calculate $a\text{.}$

Video Solution

Answer

$4$

Exercise #7

Shown below is the deltoid ABCD.

Side length BD equals 5 cm.

The area of the deltoid is 45 cm².

What is the the value of $a?$

Video Solution

Answer

$4.5$

Exercise #8

Shown below is the deltoid ABCD.

AC = 2X

DB = X

The area of the deltoid is equal to 32 cm².

Calculate DB.

Video Solution

Answer

$\sqrt{32}$

Exercise #9

Shown below is the deltoid ABCD.

The diagonal AC = X

Diagonal DB = 5

The area of the deltoid is 20 cm².

Calculate X.

Video Solution

Answer

x=8

Exercise #10

The deltoid ABCD is shown below.

AC = X

DB = 3X

The area of the deltoid is 27 cm².

Calculate the length of AC.

Video Solution

Answer

$\sqrt{18}$

Question 1

ABCD is a deltoid.

Side BM equals 4 cm.

The area of the deltoid is equal to 144 cm².

Calculate b.

Question 2

Given the deltoid ABCD

height AE formed by the diagonal extension AC

Side BE equals 5 cm

The area of the deltoid is equal to 160 cm².

Find the value of the parameter $\( b \)$

Question 3

Given the deltoid ABCD

Side length MD equals 2 cm

The area of the deltoid is equal to 200 cm².

Find the value of the parameter $\( b \)$

Question 4

Shown below is the deltoid ABCD.

Side length MD equals 3 cm.

The area of the deltoid is 180 cm².

What is the value of $b\text{?}$

Exercise #11

ABCD is a deltoid.

Side BM equals 4 cm.

The area of the deltoid is equal to 144 cm².

Calculate b.

Video Solution

Answer

$6$

Exercise #12

Given the deltoid ABCD

height AE formed by the diagonal extension AC

Side BE equals 5 cm

The area of the deltoid is equal to 160 cm².

Find the value of the parameter $b$

Video Solution

Answer

$8$

Exercise #13

Given the deltoid ABCD

Side length MD equals 2 cm

The area of the deltoid is equal to 200 cm².

Find the value of the parameter $b$

Video Solution

Answer

$20$

Exercise #14

Shown below is the deltoid ABCD.

Side length MD equals 3 cm.

The area of the deltoid is 180 cm².

What is the value of $b\text{?}$

Video Solution

Answer

$15$