Area of a Deltoid: Using additional geometric shapes

In a rectangular shopping mall they want to place a deltoid-shaped stage.

The length of the rectangle is 30 meters and the width 20 meters.

What is the area of the orange scenario?

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:

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

300 m

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.

5

Given ABCD deltoid AB=AC DC=BD

The diagonals of the deltoid intersect at the point O

Given in cm AO=12 OD=4

The area of the deltoid is equal to 48 cm².

Calculate the side CD

5 cm

The perimeter of the deltoid ABCD shown below is 30 cm².

Calculate its area.

$3\sqrt{91}$ cm²

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

Calculate x.

$x=4$

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

15 cm²

Given ABCD deltoid AB=BC DA=DC

The diagonals of the deltoid intersect at the point O

Given in cm BO=7 OC=4 AD=5

Calculate the area of the deltoid

40 cm²

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.

30 cm²

ABCD is a kite.

The area of triangle BCD is equal to 20 cm².

Calculate the area of the kite.

32 cm²

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.

66 cm²

ABCD is a kite.

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

Calculate the area of the kite.

$3\sqrt{3}$ cm²

ABCD is a parallelogram and BCEF is a kite.

$EG=2$

$GC=3$

Calculate the area of the kite

$18\sqrt{2}-6$ cm²

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?

$49\pi$ cm².

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.

$180\sqrt{5}$ cm²

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.

$6\sqrt{13}$ cm²

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?

3:26

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

8 cm²

The deltoid ABCD has an area equal to 90 cm².

If the area of the triangle BCD is equal to 18 cm², then what is the perimeter of the deltoid?

$30+2\sqrt{85}$

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.

$6\sqrt{2}x$ cm²

The perimeter of deltoid ABCD is equal to 20 cm.

$AC=\sqrt{41}-1$

Calculate the area of the deltoid.

$\sqrt{328}$ cm²