Choose language

PL, EN, ES, DE, FR, RU


Deltoid, kite concave, dart, arrowhead - diagonals, area, perimeter, sides


Calculate the diagonals of a concave deltoid, kite, side lengths, surface area, perimeter and radius of the inscribed circle. Each size can be calculated using many formulas, just indicate what data we have.



First diagonal of concave deltoid (concave kite, dart, arrowhead)

First diagonal of concave deltoid on side (a) and angle α

$$ e=a\cdot 2\sin\left(\frac{\alpha}{2}\right); $$ $$ e=2\cdot\sqrt{a^2-g^2 } $$ where $$ g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right) $$

First diagonal of concave deltoid side (b) and angle β

$$ e=b\cdot 2\sin\left(\frac{\beta}{2}\right) $$

First diagonal of the concave deltoid on the sides, the second diagonal and the angle γ

$$ e=\frac{2\cdot a\cdot b\cdot \sin\gamma}{f} $$

First diagonal of the concave deltoid on the sides, the second diagonal and the angle α

$$ e=2\cdot\sqrt{b^2-(f+g)^2} $$ gdzie $$ g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right) $$
Przekątna pierwsza deltoidu wklęsłego




Second diagonal of the concave deltoid (concave kite, dart, arrowhead)

Second diagonal of concave deltoid on sides (a) (b) and angles α & β

$$ f=a\cdot cos\left(\frac{\alpha}{2}\right)+ b\cdot cos\left(\frac{\beta}{2}\right)$$

Second diagonal of the concave deltoid on the sides (a) (b) and the first diagonal

$$ f=\sqrt{b^2-\left(\frac{e}{2}\right)^2}-\sqrt{a^2-\left(\frac{e}{2}\right)^2} $$

Second diagonal of concave deltoid with sides, first diagonal and angle γ

$$ f=\frac{2\cdot a\cdot b\cdot \sin\gamma}{e} $$

Second diagonal of the concave deltoid on the sides and angle γ

$$ f=\sqrt{a^2+b^2-2\cdot a \cdot b \cdot \cos\gamma} $$

Second diagonal of the concave deltoid on the side (a) and the angle β & γ

$$ f=\frac{a\cdot \sin\gamma}{\sin\left(\frac{\beta}{2}\right)} $$

Second diagonal of concave deltoid with sides, first diagonal and angle α

$$ f=\sqrt{b^2-\left(\frac{e}{2}\right)^2}-g $$ where $$ g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right) $$
Przekątna druga deltoidu wklęsłego







Surface area of the concave deltoid (concave kite, dart, arrowhead)

Area of the concave deltoid on the sides (a)(b) and angles α & β

$$ S=\frac{a^2\cdot \sin\alpha}{2}+\frac{b^2\cdot\sin\beta}{2} $$

Area of the concave deltoid on the sides (a)(b) and the angle γ

$$ S=a\cdot b\cdot \sin\gamma $$

Area of the concave deltoid from the diagonals

$$ S=\frac{e\cdot f}{2} $$
Pole powierzchni deltoidu wklęsłego



Concave deltoid circumference (concave kite, dart, arrowhead)

Concave deltoid circumference from the sides

$$ L = 2a + 2b $$

Concave deltoid circumference from the shorter diagonal and the angle(α) & (β)

$$ L = \frac{e}{\sin\left(\frac{\beta}{2}\right)}+\frac{e}{\sin\left(\frac{\alpha}{2}\right)} $$
Obwód deltoidu wklęsłego



Sides of the concave deltoid (concave kite, dart, arrowhead)

Side (a) of the concave deltoid from the shorter diagonal and angle α

$$ a=\frac{e}{2\cdot\sin\left(\cfrac{\alpha}{2}\right)} $$

Side (b) of the concave deltoid from the shorter diagonal and angle β

$$ b=\frac{e}{2\cdot\sin\left(\cfrac{\beta}{2}\right)} $$

Side (a) of the concave deltoid on the side (b) and angles α & β

$$ a=\frac{b\cdot \sin\left(\cfrac{\beta}{2}\right)}{\sin\left(\cfrac{\alpha}{2}\right)} $$

Side (b) of the concave deltoid on the side (a) and angles α & β

$$ b=\frac{a\cdot \sin\left(\cfrac{\alpha}{2}\right)}{\sin\left(\cfrac{\beta}{2}\right)} $$
Boki deltoidu wklęsłego






Concave deltoid, concave kite, dart, arrowhead

Deltoid - is a quadrilateral whose four sides can be grouped into two pairs of equal length adjacent sides. The sides of the same length have a common vertex.
Deltoid can be convex or concave.

Concave deltoid, also known as an concave kite, dart, arrowhead - is a deltoid in which the internal angle between the shorter sides is greater than 180 °.

Deltoid wklęsły


Concave deltoid has the following properties:
  1. The sum of the measures of all the internal angles of the deltoid is 2Π $$ \alpha+\beta+2\cdot\gamma=360^\circ $$
  2. Formula for the first diagonal of the concave deltoid on the side (a) and the angle α
    3. $$ e=a\cdot 2\sin\left(\frac{\alpha}{2}\right); $$ $$ e=2\cdot\sqrt{a^2-g^2 } $$ gdzie $$ g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right) $$
  3. Formula for the first diagonal of the concave deltoid on the side (b) and the angle β
    4. $$ e=b\cdot 2\sin\left(\frac{\beta}{2}\right) $$
  4. Formula for the first diagonal of the concave deltoid on the sides, the second diagonal and the angle γ
    5. $$ e=\frac{2\cdot a\cdot b\cdot \sin\gamma}{f} $$
  5. Formula for the first diagonal of the concave deltoid on the sides, the second diagonal and the angle α
    6. $$ e=2\cdot\sqrt{b^2-(f+g)^2} $$ gdzie $$ g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right) $$
  6. Second diagonal of concave deltoid on sides (a) (b) and angles α & β
    7. $$ f=a\cdot cos\left(\frac{\alpha}{2}\right)+ b\cdot cos\left(\frac{\beta}{2}\right)$$
  7. Formula for the second diagonal of the concave deltoid from the sides (a) (b) and the first diagonal
    8. $$ f=\sqrt{b^2-\left(\frac{e}{2}\right)^2}-\sqrt{a^2-\left(\frac{e}{2}\right)^2} $$
  8. Formula for the second diagonal of the concave deltoid from the sides, the first diagonal and the angle γ
    9. $$ f=\frac{2\cdot a\cdot b\cdot \sin\gamma}{e} $$
  9. Formula for the second diagonal of the concave deltoid from the sides and the angle γ
    10. $$ f=\sqrt{a^2+b^2-2\cdot a \cdot b \cdot \cos\gamma} $$
  10. Formula for the second diagonal of the concave deltoid on the side (a) and the angle β & γ
    11. $$ f=\frac{a\cdot \sin\gamma}{\sin\left(\frac{\beta}{2}\right)} $$
  11. Formula for the second diagonal of the concave deltoid from the sides, the first diagonal and the angle α
    12. $$ f=\sqrt{b^2-\left(\frac{e}{2}\right)^2}-g $$ gdzie $$ g=a\cdot \sin \left(\frac{\alpha}{2}-90^\circ\right) $$
  12. Formula for Area of the concave deltoid on the sides (a) (b) and angles α & β
    13. $$ S=\frac{a^2\cdot \sin\alpha}{2}+\frac{b^2\cdot\sin\beta}{2} $$
  13. Formula for the Area of the concave deltoid on the sides (a)(b) and the angle γ
    14. $$ S=a\cdot b\cdot \sin\gamma $$
  14. Formula for the Area of the concave deltoid from the diagonals
    15. $$ S=\frac{e\cdot f}{2} $$
  15. Formula for the perimeter of the concave deltoid on the sides
    16. $$ L = 2a + 2b $$
  16. Formula for the circumference of the concave deltoid from the shorter diagonal and the angle(α) & (β)
    17. $$ L = \frac{e}{\sin\left(\frac{\beta}{2}\right)}+\frac{e}{\sin\left(\frac{\alpha}{2}\right)} $$
  17. Formula on the side (a) of the concave deltoid with the shorter diagonal and angle α
    18. $$ a=\frac{e}{2\cdot\sin\left(\cfrac{\alpha}{2}\right)} $$
  18. Formula on the side (b) of the concave deltoid with the shorter diagonal and angle β
    19. $$ b=\frac{e}{2\cdot\sin\left(\cfrac{\beta}{2}\right)} $$
  19. Formula for the Side (a) of the deltoid on the concave side (b) and angles α & β
    20. $$ a=\frac{b\cdot \sin\left(\cfrac{\beta}{2}\right)}{\sin\left(\cfrac{\alpha}{2}\right)} $$
  20. Formula on the side (b) of the concave deltoid on the side (a) and angles α & β
    21. $$ b=\frac{a\cdot \sin\left(\cfrac{\alpha}{2}\right)}{\sin\left(\cfrac{\beta}{2}\right)} $$





Users of this calculator also used

Rail Fence, Zig-Zag - encoder / decoder

Rail Fence, Zig-Zag cipher online encoder and decoder. Encrypt and decrypt any cipher created in a Rail Fence, Zig-Zag cipher.

Bicycle tire pressure calculator

With this calculator, you will calculate the exact tire pressure required for your bicycle tires on the front and rear wheels depending on the load, wheel size, bicycle weight, etc.

Matrix 2x2 calculator

Thanks to the mathematical calculator, you can easily calculate the determinant of the matrix, find the complement matrix, the transposed matrix, and the inverse matrix.

Average absolute deviation, or mean absolute deviation (MAD)

With this calculator you will calculate the average absolute deviation, or mean absolute deviation (MAD), of a data set is the average of the absolute deviations from a central point.

Heart attack risk

Thanks to the calculator, you can use several factors to check the degree of risk of a heart attack in the next ten years.

Text analyzer, number of words, number of letters, number of lines

Thanks to the calculator you can calculate the number of letters, the number of words, the number of characters and the number of paragraphs in any text.

Basal metabolic rate (BMR) - calculator

Using the calculator, you will calculate the basic metabolic rate (BMR-basal metabolic rate) and the amount of calories needed to supplement, i.e. burned by the body on an empty stomach (in the morning, without a meal), in physical and mental peace.



Online calculator

C
M+
M-
MR
log
10x
MS
MC
asin
acos
atan
ex
sin-1
cos-1
tan-1
ln
sin
cos
tan
π
√
x²
1/x
x!
xM
(
)
exp
7
8
9
÷
4
5
6
×
1
2
3
-
0
·
=
+
C
M+
M-
sin
sin-1
asin
MC
MS
MR
cos
cos-1
acos
log
ln
10x
tan
tan-1
atan
π
e
ex
exp
1/x
x!
7
8
9
(
)
xM
4
5
6
-
÷
x²
1
2
3
+
×
√
0
·
=