Calculating Areas of Special Triangles Where Is Necessary to Find the Height, and/or the Base.

The area for a triangle is one half the product of the base by the height; nevertheless, sometimes this is not possible to apply right away. In those cases we need to use special right triangles (30°-60°-90°, or 45°-45°-90°), and/or Pythagorean Theorem, or trigonometry; to find the base, and/or the height for a particular problem.

We are aware that these are topics that present sometimes difficulties for some students, that is why we strive to develop the problem solving process in a detailed step by step mode, and without skipping, or implying that the student should know it. Whether you are a struggling student, or an advanced one; you will find the lesson to be doable, interesting, and challenging fun! One alternative each time an example is shown is that you will be allowed to solve very similar problems on the screen with the marker tools menu and writing the solution on the screen (Stylus or your finger since tablets nowadays on the market allow it).

Lesson's Content

Lesson's Glossary

Altitude
Height

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

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.

Angle bisector
A ray that is in the interior of an angle and forms two equal angles with the sides of that angle. Area
The amount of space taken up in a plane by a figure.

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.

Cosine
Ratio determined by the hypotenuse in a right triangle and a side adjacent to a reference angle.

Equilateral triangle
A triangle whose sides are equal in length.

Isosceles triangle
A triangle with two sides of equal length.

Median
The segment connecting the vertex of an angle in a triangle to the midpoint of the side opposite it.

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

Obtuse triangle
A triangle with one acute angle.

Perpendicular bisector
The bisector of a segment perpendicular to it.

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

Pythagorean theorem a2 + b2 = c2.
The Pythagorean theorem states that if you have a right triangle, then the square built on the hypotenuse is equal to the sum of the squares built on the other two sides.

Right triangle
A triangle that has a 90 degree angle.

Sine
Ratio of the length of the opposite side to a reference angle in a right triangle and the hypotenuse. Opposite/hypotenuse.

Scalene triangle
A triangle with no equilateral sides.

Triangle
A polygon with three sides.

Tangent
The ratio of the length of the opposite side of a reference angle to the adjacent side to the same angle. Opposite over adjacent.

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