Rectangular trapezoid - Information

Trapezoid – a quadrilateral having at least one pair of parallel sides; The (selected) pair of parallel sides are called the bases, the remaining sides are called the legs, the distance between the bases is called the height of the trapezoid. Some colloquial definitions define a trapezoid as a quadrilateral with only one pair of parallel sides and, accordingly, the parallelogram is not a trapezoid. The sum of the angles on the same legs is 180°.

Rectangular trapezoid is a trapezoid with two right angles.

Rectangular trapezoid has the following properties:

1. Trapezoid is a convex figure.
2. Sum of the measures of all interior angles is 2Π (360 °), and the sum of the measures of two adjacent internal angles lying on the same leg is Π, $$ \alpha + \delta = 180° $$
3. Formula for the angle α $$ \alpha = 90° - \arccos( \frac{ b^2 + d^2 - (a-c)^2 }{ 2 \cdot b \cdot d }) $$
4. Formula for the first diagonal of a rectangular trapezoid from sides (c) and (d)
$$ e=\sqrt{c^2+d^2} $$
5. Formula for the first diagonal of a rectangular trapezoid from sides (a)(b)(c)(d)
$$ e= \sqrt{\frac{ac^2 - a^2c - ab^2 + d^2c}{c-a}} $$
6. Formula for the second diagonal of a rectangular trapezoid from sides (a) and (d)
$$ f=\sqrt{a^2+d^2} $$
7. Formula for the second diagonal of a rectangular trapezoid from sides (a)(b)(c)(d)
$$ f= \sqrt{\frac{ac^2 - a^2c - ad^2 + cb^2}{c-a}} $$
8. Formula for the height of the rectangular trapezoid from sides (a)(c) and area
$$ h=\frac{2S}{a+c} $$
9. Formula for the height of the rectangular trapezoid from leg (b) and angle α or β
$$ h = b \cdot \sin \alpha = b \cdot \sin \beta $$
10. Height of the rectangular trapezoid from sides (a)(b)(c)
$$ h = \sqrt{b^2 - (a-c)^2} $$
11. Formula for the area of the rectangular trapezoid from sides (a)(c) i (d)
$$ S={\frac {a+c}{2}}\cdot d $$
12. Formula for the area of the rectangular trapezoid from sides (a)(b)(c) and angle(α)
$$ S=\frac{1}{2}\cdot\left(a+c\right)\cdot b\cdot \sin\alpha $$
13. Formula for the area of the rectangular trapezoid from sides (b)(c)(d) and angle(α)
$$ S=\frac{b^2 \cdot \sin 2\alpha}{4}+ c \cdot d $$
14. Formula for the perimeter of the rectangular trapezoid from sides
$$ L = a + b + c + d $$
15. Formula for the perimeter of the rectangular trapezoid from sides (a)(c)(d) and angles(α) oraz (β)
$$ L = a+c+d+(\frac{1}{\sin(\alpha)}+\frac{1}{\sin(\beta)}) $$
16. Formula for the side (a) rectangular trapezoid from sides (b)(c)(d)
$$ a=c+\sqrt{b^2-d^2} $$
17. Formula for the side (b) rectangular trapezoid from sides (a)(c)(d)
$$ b=\sqrt{(a-c)^2+d^2} $$
18. Formula for the side (c) rectangular trapezoid from sides (a)(b)(d)
$$ c=a-\sqrt{b^2-d^2} $$
19. Formula for the side (d) rectangular trapezoid from sides (a)(b)(c)
$$ d=\sqrt{b^2-(a-c)^2} $$
20. Formula for the midline (median , midsegment) of the trapezoid $$ m=\frac {a+c}{2} $$