Summary: Using Properties of Rectangles, Triangles, and Trapezoids

Key Concepts

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

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.

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.