# Acute Trapezoid

Written by Jerry Ratzlaff on . Posted in Plane Geometry

• Acute triangle (a two-dimensional figure) has two adjacent acute angles on the longer base edge.
• Acute angle measures less than 90°.
• Obtuse angle measures more than 90°.
• a & c are bases
• b & d are legs
• a ∥ c
• a ≠ c
• b ≠ d
• ∠A, ∠D < 90°
• ∠B, ∠C > 90°
• ∠A + ∠B = 180°
• ∠C + ∠D = 180°

## formulas that use Area of an Acute Trapezoid

 $$\large{ A_{area} = h \; \left( \frac{c \;+\; a}{2 } \right) }$$ $$\large{ A_{area} = m\; h }$$

### Where:

$$\large{ A_{area} }$$ = area

$$\large{ h }$$ = height

$$\large{ m }$$ = midline

$$\large{ a, b, c, d }$$ = edge

## formulas that use Midline of an Acute Trapezoid

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

### Where:

$$\large{ m }$$ = midline

$$\large{ a, b, c, d }$$ = edge

## formulas that use Perimeter of an Acute Trapezoid

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

### Where:

$$\large{ P }$$ = perimeter

$$\large{ h }$$ = height

$$\large{ a, b, c, d }$$ = edge