# Calculating Areas of Rhombi and Trapezoids.

### We are going to go from very simple problems, where all we do is substitute to up to problems where we solve a quadratic equation, or solve a system of linear two variable equations. You won't be left in the limbo, since we won't skip intermediate steps. At the same time you are going to check for understanding when solving the suggested problems. You will grow geometrically speaking!

Lesson's Content

 Lesson In PDF Format (no animations)

Lesson's Glossary

Altitude of a triangle (height)
The perpendicular segment from a vertex to the line containing the opposite side of a triangle.

Altitude of a trapezoid (height)
The distance between the bases of a trapezoid.

Angle
Geometry shape formed by two rays (initial and ending sides of the angle) that share a common endpoint called the vertex. You may name an angle using the vertex, or a point in each ray and the vertex label in the center.

Area
The amount of space taken up in a plane by a figure.

Base
The side of an isosceles triangle whose endpoints are the vertices of the base angles.

Base angle
The angle opposite one of the equilateral sides in an isosceles triangle.

Base of a trapezoid
The parallel sides of a trapezoid.

Equilateral triangle
A triangle whose sides are equal in length.

Isosceles triangle
A triangle with two sides of equal length.

Isosceles trapezoid
Trapezoid with two non-congruent and non-parallel sides.

Obtuse angle
An angle whose measure is greater than 90 but less than 180 degrees.

Obtuse triangle
A triangle with one acute angle.

Parallelogram
Any quadrilateral with two pairs of opposite sides parallel.

Polygon
It is a closed plane figure with a least three straight segments as sides.

A four-sided polygon.

Right triangle
A triangle that has a 90 degree angle.

Rhombus
Any parallelogram with 4 congruent sides.

Scalene triangle
A triangle with no equilateral sides.

Square

Triangle
A polygon with three sides.

Trapezoid
Quadrilateral with exactly one pair of parallel sides.

Interactive Geometric Applets: Relevant Theorems.

A rhombus has all the properties for a parallelogram. You have opposite

sides congruent, and parallel. It has diagonals that bisect each other.

Its diagonals are perpendicular, and angle bisectors.

Review these properties before solving areas for rhombi.

A square is a parallelogram with all properties of the rhombus and the rectangle.

You have that all squares are a special rhombus, and a special rectangle; but not all

rhombi, and rectangles are squares. Reviewing it will help you finding areas for squares.

The Isosceles Trapezoid is different to other quadrilaterals. You have one pair of parallel sides,

and one pair of congruent sides. Opposite angles are supplementary, and top and bottom

base angles are congruent. All these reasons sets it apart from the parallelograms.

It would be very helpful to review them before solving for areas in trapezoids.

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