Trapezoid

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• A trapezoid has two edges ($$b$$ and $$d$$) that are parallel lines.
• The two parallel edges ($$b$$ and $$d$$) are called the base of the trapezoid.
• Trapezoid is a quadrilateral with only one pair of parallel edges.
• Edge $$a$$ and $$c$$ are called legs
• Edge $$\;a = c$$
• Angle $$\;A = D$$
• Angle $$\;B = C$$
• 2 diagonals
• 4 edges
• 4 vertexs

Edge formula

$$a = P-b-c-d$$

$$b = P-c-d-a$$

$$b = 2 \frac {A}{h} -d$$

$$c = P-d-a-b$$

$$d = P-a-b-c$$

$$d = 2 \frac {A}{h} -b$$

Where:

$$a$$ = edge

$$b$$ = edge

$$c$$ = edge

$$d$$ = edge

$$h$$ = height

$$P$$ = perimeter

$$A$$ = area

Height formula

$$h = 2 \frac {A} {a+b}$$

Where:

$$h$$ = height

$$a$$ = edge

$$b$$ = edge

$$A$$ = area

Perimeter formula

$$P=a+b+c+d$$

Where:

$$P$$ = perimeter

$$a$$ = edge

$$b$$ = edge

$$c$$ = edge

$$d$$ = edge

Area formula

$$A=\frac{h}{2}(b-d)$$

$$A=\frac{b+d}{2} h$$

Where:

$$A$$ = area

$$b$$ = edge

$$d$$ = edge

$$h$$ = height