Area of a Deltoid: Using additional geometric shapes

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 variables Applying the formula Finding Area based off Perimeter and Vice Versa Calculate The Missing Side based on the formula

Question 1

A deltoid-shaped stage is to be built in a rectangular field.

The length of the field is 30 m and the width is 20 m.

What is the area of the stage shaded in orange?

Question 2

In an amusement park with a rectangle shape, they decided to place part of the floor of its surface (referring to the shape of the deltoid).

The length of the tile is 3 meter and its width 2 meter.

The length of the garden is 10 meters and its width 6 meters.

Calculate how many tiles you will need to use to complete the deltoid shape.

Question 3

Below is a deltoid with a length 2 times its width and an area equal to 16 cm².

Calculate x.

Question 4

ABCD is a deltoid, EFBD is a square whose area is 25 cm²

Given that GC is equal to 7 cm

Calculate the area of the deltoid.

Question 5

ABCD is a kite.

AB = AD

ABD has an area of 30 cm².
EC is equal to 6 cm.
AE is equal to 5 cm.

Calculate the area of the kite.

Examples with solutions for Area of a Deltoid: Using additional geometric shapes

Exercise #1

A deltoid-shaped stage is to be built in a rectangular field.

The length of the field is 30 m and the width is 20 m.

What is the area of the stage shaded in orange?

Video Solution

Step-by-Step Solution

We can calculate the area of rectangle ABCD like so:

$20\times30=600$

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

Finally, we can calculate the area of deltoid PMNK as follows:

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

Answer

300 m

Exercise #2

In an amusement park with a rectangle shape, they decided to place part of the floor of its surface (referring to the shape of the deltoid).

The length of the tile is 3 meter and its width 2 meter.

The length of the garden is 10 meters and its width 6 meters.

Calculate how many tiles you will need to use to complete the deltoid shape.

Video Solution

Answer

Exercise #3

Below is a deltoid with a length 2 times its width and an area equal to 16 cm².

Calculate x.

Video Solution

Answer

$x=4$

Exercise #4

ABCD is a deltoid, EFBD is a square whose area is 25 cm²

Given that GC is equal to 7 cm

Calculate the area of the deltoid.

Video Solution

Answer

30 cm²

Exercise #5

ABCD is a kite.

AB = AD

ABD has an area of 30 cm².
EC is equal to 6 cm.
AE is equal to 5 cm.

Calculate the area of the kite.

Video Solution

Answer

66 cm²

Question 1

ABCD is a kite

ABED is a trapezoid with an area of 22 cm².

AC is 6 cm long.

Calculate the area of the kite.

Question 2

ABCD is a kite.

BC is the radius of a circle with an area of $4\pi$ cm.

Calculate the area of the kite.

Question 3

ABCD is a kite.

O is the center of the circle whose diameter is DE and which has an area of $36\pi$ cm².

The area of a circle whose radius is AE is 5 times greater than the area of the circle O.

$EC=\frac{3}{2}AE$

Calculate the area of the kite.

Question 4

ABCD is a kite.

The area of triangle BCD is equal to 20 cm².

Calculate the area of the kite.

Question 5

ABCD is a parallelogram and BCEF is a kite.

$$ EG=2 $$

$$ GC=3 $$

Calculate the area of the kite

Exercise #6

ABCD is a kite

ABED is a trapezoid with an area of 22 cm².

AC is 6 cm long.

Calculate the area of the kite.

Video Solution

Answer

$6\sqrt{13}$ cm²

Exercise #7

ABCD is a kite.

BC is the radius of a circle with an area of $4\pi$ cm.

Calculate the area of the kite.

Video Solution

Answer

$3\sqrt{3}$ cm²

Exercise #8

Video Solution

Answer

$180\sqrt{5}$ cm²

Exercise #9

ABCD is a kite.

The area of triangle BCD is equal to 20 cm².

Calculate the area of the kite.

Video Solution

Answer

32 cm²

Exercise #10

ABCD is a parallelogram and BCEF is a kite.

$EG=2$

$GC=3$

Calculate the area of the kite

Video Solution

Answer

$18\sqrt{2}-6$ cm²

Question 1

Given the deltoid ABCD and the circle that its center O on the diagonal BC

Area of the deltoid 28 cm² AD=4

What is the area of the circle?

Question 2

Given the deltoid ABCD

and the deltoid AFCE whose area is 20 cm².

The ratio between AO and OC is 1:3

the angle ADC⦠. is equal to the angle ACD⦠.

AD is equal to 8

Calculate the area of the triangle CEF

Question 3

ABCD is a deltoid with an area of 58 cm².

DB = 4

AE = 3

What is the ratio between the circles that have diameters formed by AE and and EC?

Question 4

ABCD is a kite.

BD is the diagonal of a square that has an area equal to 36 cm².

$$ AC=2x $$

Express the area of the kite in terms of X.

Question 5

Given the triangle ABC and the deltoid ADEF

The height of the triangle is 4 cm

The base of the triangle is greater by 2 than the height of the triangle.

Segment FD cut to the middle

Calculate the area of the deltoid ADEF

Exercise #11

Given the deltoid ABCD and the circle that its center O on the diagonal BC

Area of the deltoid 28 cm² AD=4

What is the area of the circle?

Video Solution

Answer

$49\pi$ cm².

Exercise #12

Given the deltoid ABCD

and the deltoid AFCE whose area is 20 cm².

The ratio between AO and OC is 1:3

the angle ADC⦠. is equal to the angle ACD⦠.

AD is equal to 8

Calculate the area of the triangle CEF

Video Solution

Answer

15 cm²

Exercise #13

ABCD is a deltoid with an area of 58 cm².

DB = 4

AE = 3

What is the ratio between the circles that have diameters formed by AE and and EC?

Video Solution

Answer

3:26

Exercise #14

ABCD is a kite.

BD is the diagonal of a square that has an area equal to 36 cm².

$AC=2x$

Express the area of the kite in terms of X.

Video Solution

Answer

$6\sqrt{2}x$ cm²

Exercise #15

Given the triangle ABC and the deltoid ADEF

The height of the triangle is 4 cm

The base of the triangle is greater by 2 than the height of the triangle.

Segment FD cut to the middle

Calculate the area of the deltoid ADEF

Video Solution

Answer

8 cm²