# Right Trapezoid

on . Posted in Plane Geometry

• Right trapezoid (a two-dimensional figure) is a trapezoid with only one pair of parallel edges and two adjacent right angles.
• Acute angle is an angle that measures less than 90°.
• Obtuse angle is an angle that measures more than 90°.
• a & c are bases
• b & d are legs
• a ∥ c
• a ≠ c
• b ≠ d
• ∠A < 90°
• ∠B > 90°
• ∠C = ∠D
• ∠A + ∠B = 180°
• ∠C + ∠D = 180°

## Angle of a Right Trapezoid formulas

$$\large{ x = 90° - arccos \; \frac{ d^2 \;+\; b^2 \;-\; \left(a \;-\; c \right)^2 }{ 2\;d\;b } }$$

$$\large{ y = 180° - x }$$

Symbol English Metric
$$\large{ x }$$ = acute angles $$\large{ deg}$$ $$\large{ rad}$$
$$\large{ y }$$ = obtuce angles $$\large{ deg}$$ $$\large{ rad}$$
$$\large{ a, b, c, d }$$ = edge $$\large{ in}$$ $$\large{ mm }$$

## Area of a Right Trapezoid formula

$$\large{ A_{area} = \frac{1}{2} \; d \; \left( a + c \right) }$$
Symbol English Metric
$$\large{ A_{area} }$$ = area $$\large{ in^2}$$ $$\large{ mm^2}$$
$$\large{ a, b, c, d }$$ = edge $$\large{ in}$$ $$\large{ mm }$$

## Diagonal of a Trapezoid formulas

$$\large{ d' = \sqrt{c^2+d^2} }$$

$$\large{ D' = \sqrt{a^2+d^2} }$$

Symbol English Metric
$$\large{ d', D' }$$ = diagonal $$\large{ in}$$ $$\large{ mm }$$
$$\large{ a, b, c, d }$$ = edge $$\large{ in}$$ $$\large{ mm }$$

## Midline of a Right Trapezoid formula

$$\large{ m = \frac{a \;+\; c}{2} }$$
Symbol English Metric
$$\large{ m }$$ = midline $$\large{ in}$$ $$\large{ mm }$$
$$\large{ a, b, c, d }$$ = edge $$\large{ in}$$ $$\large{ mm }$$

## Perimeter of a Trapezoid formula

$$\large{ P = a + b + c + d }$$
Symbol English Metric
$$\large{ P }$$ = perimeter $$\large{ in}$$ $$\large{ mm }$$
$$\large{ a, b, c, d }$$ = edge $$\large{ in}$$ $$\large{ mm }$$

## Side of a Right Trapezoid formulas

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

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

Symbol English Metric
$$\large{ b, d }$$ = edge $$\large{ in}$$ $$\large{ mm }$$
$$\large{ a, c }$$ = edge $$\large{ in}$$ $$\large{ mm }$$ 