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# Rectangular trapezoid calculator - diagonals, area, perimeter, sides lenght

Rectangular trapezoid calculator will help you calculate the long diagonal of the trapezoid, the short diagonal of the trapezoid, the side length, height, area and perimeter of the trapezoid.

## First diagonal of the rectangular trapezoid

### First diagonal of the trapezoid from sides (c) and (d)

$$e=\sqrt{c^2+d^2}$$

### First diagonal of the trapezoid from sides (a)(b)(c)(d)

$$e= \sqrt{\frac{ac^2 - a^2c - ab^2 + d^2c}{c-a}}$$

## Second diagonal of the rectangular trapezoid

### Second diagonal of the trapezoid from sides (a) i (d)

$$f=\sqrt{a^2+d^2}$$

### Second diagonal of the trapezoid from the sides (a)(b)(c)(d)

$$f= \sqrt{\frac{ac^2 - a^2c - ad^2 + cb^2}{c-a}}$$

## Height of the rectangular trapezoid

### Height of the trapezoid from the sides (a)(c) and area

$$h=\frac{2S}{a+c}$$

### Height of the trapezoid from leg (b) and angle α or β

$$h = b \cdot \sin \alpha = b \cdot \sin \beta$$

### Height of the trapezoid from the sides (a)(b)(c)

$$h = \sqrt{b^2 - (a-c)^2}$$

## Area of the rectangular trapezoid

### Area of the trapezoid from sides (a)(c) i (d)

$$S={\frac {a+c}{2}}\cdot d$$

### Area of the trapezoid from the sides (a)(b)(c) and the angle(α)

$$S=\frac{1}{2}\cdot\left(a+c\right)\cdot b\cdot \sin\alpha$$

### Area of the trapezoid from sides (b)(c)(d) and angle(α)

$$S=\frac{b^2 \cdot \sin 2\alpha}{4}+ c \cdot d$$

## Perimeter of the rectangular trapezoid

### Perimeter of the trapezoid from the sides

$$L = a + b + c + d$$

### Perimeter of the trapezoid from the sides (a)(c)(d) and angles(α) and (β)

$$L = a+c+d+(\frac{1}{\sin(\alpha)}+\frac{1}{\sin(\beta)})$$

## Sides of a rectangular trapezoid

### Lenght side (a) trapezoid from sides (b)(c)(d)

$$a=c+\sqrt{b^2-d^2}$$

### Lenght leg (b) trapezoid from sides (a)(c)(d)

$$b=\sqrt{(a-c)^2+d^2}$$

### Lenght side (c) trapezoid from sides (a)(b)(d)

$$c=a-\sqrt{b^2-d^2}$$

### Lenght leg (d) trapezoid from sides (a)(b)(c)

$$d=\sqrt{b^2-(a-c)^2}$$

## Midline (median , midsegment) of the rectangular trapezoid

### Midline (median , midsegment) of the trapezoid

$$m=\frac {a+c}{2}$$

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)
5. $$e=\sqrt{c^2+d^2}$$
6. Formula for the first diagonal of a rectangular trapezoid from sides (a)(b)(c)(d)
7. $$e= \sqrt{\frac{ac^2 - a^2c - ab^2 + d^2c}{c-a}}$$
8. Formula for the second diagonal of a rectangular trapezoid from sides (a) and (d)
9. $$f=\sqrt{a^2+d^2}$$
10. Formula for the second diagonal of a rectangular trapezoid from sides (a)(b)(c)(d)
11. $$f= \sqrt{\frac{ac^2 - a^2c - ad^2 + cb^2}{c-a}}$$
12. Formula for the height of the rectangular trapezoid from sides (a)(c) and area
13. $$h=\frac{2S}{a+c}$$
14. Formula for the height of the rectangular trapezoid from leg (b) and angle α or β
15. $$h = b \cdot \sin \alpha = b \cdot \sin \beta$$
16. Height of the rectangular trapezoid from sides (a)(b)(c)
17. $$h = \sqrt{b^2 - (a-c)^2}$$
18. Formula for the area of the rectangular trapezoid from sides (a)(c) i (d)
19. $$S={\frac {a+c}{2}}\cdot d$$
20. Formula for the area of the rectangular trapezoid from sides (a)(b)(c) and angle(α)
21. $$S=\frac{1}{2}\cdot\left(a+c\right)\cdot b\cdot \sin\alpha$$
22. Formula for the area of the rectangular trapezoid from sides (b)(c)(d) and angle(α)
23. $$S=\frac{b^2 \cdot \sin 2\alpha}{4}+ c \cdot d$$
24. Formula for the perimeter of the rectangular trapezoid from sides
25. $$L = a + b + c + d$$
26. Formula for the perimeter of the rectangular trapezoid from sides (a)(c)(d) and angles(α) oraz (β)
27. $$L = a+c+d+(\frac{1}{\sin(\alpha)}+\frac{1}{\sin(\beta)})$$
28. Formula for the side (a) rectangular trapezoid from sides (b)(c)(d)
29. $$a=c+\sqrt{b^2-d^2}$$
30. Formula for the side (b) rectangular trapezoid from sides (a)(c)(d)
31. $$b=\sqrt{(a-c)^2+d^2}$$
32. Formula for the side (c) rectangular trapezoid from sides (a)(b)(d)
33. $$c=a-\sqrt{b^2-d^2}$$
34. Formula for the side (d) rectangular trapezoid from sides (a)(b)(c)
35. $$d=\sqrt{b^2-(a-c)^2}$$
36. Formula for the midline (median , midsegment) of the trapezoid $$m=\frac {a+c}{2}$$