Calculating Areas of Rhombi and Trapezoids.

Did you know that when working with plane geometry in middle school, or high school you may encounter problems to calculate areas of trapezoids, or rhombi that will give place to a quadratic equation, or a systems of equations in the solution process?

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!

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.

Quadrilateral
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
An equilateral and equiangular quadrilateral.

Triangle
A polygon with three sides.

Trapezoid
Quadrilateral with exactly one pair of parallel sides.
 

PURCHASE INFORMATION

Algebra, Geometry, and Basic Math Lessons, and Lesson Plans

In the solution of area problems for trapezoids, or rhombi; you will be required

to use the Pythagorean Theorem to find line segments that are part of the sides, diagonals,

or height in the figures. This applet allows you to review the theorem.

You may view the animation by dragging any of the vertices. Pay attention

to the red, and green areas for the squares of the legs, and check how they

perfectly fit in the square of the hypotenuse.

 

 

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