Summary: Using Properties of Rectangles, Triangles, and Trapezoids

Key Concepts

• Properties of Rectangles
  • Rectangles have four sides and four right ($90^\circ$) angles.
  • The lengths of opposite sides are equal.
  • The perimeter, $P$ , of a rectangle is the sum of twice the length and twice the width.
    • $P=2L+2W$
  • The area, $A$ , of a rectangle is the length times the width.
    • $A=L\cdot W$
• Triangle Properties
  • For any triangle $\Delta ABC$ , the sum of the measures of the angles is $180^\circ$.
    • $m\angle A+m\angle B+m\angle C=180^\circ$
  • The perimeter of a triangle is the sum of the lengths of the sides.
    • $P=a+b+c$
  • The area of a triangle is one-half the base, $b$, times the height, $h$.
    • $A=\Large\frac{1}{2}\normalsize bh$
• Trapezoid properties
  • A trapezoid has a larger base, $B$, and a smaller base, $b$. The height $h$ is the distance between the bases.
  • The formula for the area of a trapezoid is one-half the height, $h$, times the sum of the big base, $B$, plus the little base, $b$.
    • ${\text{Area}}_{\text{trapezoid}}=\Large\frac{1}{2}\normalsize h\left(b+B\right)$

Glossary

area

The area is a measure of the surface covered by a figure.

equilateral triangle

A triangle with all three sides of equal length is called an equilateral triangle.

isosceles triangle

A triangle with two sides of equal length is called an isosceles triangle.

perimeter

The perimeter is a measure of the distance around a figure.

rectangle

A rectangle is a geometric figure that has four sides and four right angles.

trapezoid

A trapezoid is four-sided figure, a quadrilateral, with two sides that are parallel and two sides that are not.

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