Lesson 2: Area - Area of Triangles

   Constructing Knowledge

Recall that the formula for the area of a triangle is:

\(\begin{align} \text{Area}_{triangle}&=\frac{\text{base}\times \text{height}}{2} \\ \\ &=\frac{1}{2}\times \text{base}\times \text{height} \\ \\ &=\frac{bh}{2} \\ \\ \text{A}_{triangle}&=\frac{1}{2}bh \\ \end{align}\)

Occasionally in a scalene triangle, the height will be outside of the triangle. Be sure to look for the right angle symbol as the height is measured at a 90° angle from the base.



When using a formula to calculate area, follow these basic steps:

  1. State the formula being used to solve the problem.
  2. Substitute known values for the variables.
  3. Solve for the unknown (remember to include proper squared units in your answer).

Remember that with all area calculations, all dimensions must be in the same unit of measure prior to substituting their values into the formula.

   Multimedia

A video demonstrating calculating the area of a triangle is provided.



EXAMPLE 1

Determine the area of a triangle whose base is 3 inches and whose height is 11 inches.

Solution


\(\begin{align} \text{A}_{triangle}&=\frac{bh}{2} \\ \\ &=\frac{3\,\text{in}\times 11\,\text{in}}{2} \\ \\ &=16.5\,\text{in}^2 \\ \end{align}\)

The area of the triangle is 16.5 in2.

EXAMPLE 2

Determine the area of the triangular park shown below.

Solution


\(\begin{align} \text{A}_{triangle}&=\frac{bh}{2} \\ \\ &=\frac{10\,\text{km}\times 5\,\text{km}}{2} \\ \\ &=25\,\text{km}^2 \\ \end{align}\)

The park has an area of 25 km2.


Now, it is your turn! Complete the questions in your Chapter 7, Lesson 2 Practice Makes Perfect that refer to Area of Triangles.



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