Topics
7. Polygons
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United States of AmericaVirginia
Grade 6

7.05 Area of triangles

Lesson
Practice

Area of triangles

Exploration

Use the 'base' and 'height' sliders to adjust the dimensions of the triangle. Then use the 'Slide to create a parallelogram' slider to create a parallelogram.

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  1. Create several different types of triangles and look at the parallelogram that is created. What do you think the relationship between the area of the triangle and area of parallelogram is?
  2. What is the formula for the area of a parallelogram?
  3. What do you think the formula for the area of a triangle might be?
A parallelogram with diagonal that will show 2 congruent triangle. Ask your teacher for more information.

If we were to cut a parallelogram along one of its diagonals, we would get two congruent triangles. Each of these triangles will have half the area of the parallelogram.

So we can develop a formula for the area of a triangle by multiplying the formula for the area of a parallelogram by \dfrac{1}{2}.

The formula for the area of a triangle is:

\displaystyle A= \dfrac{1}{2} b h
\bm{A}
Area of the triangle
\bm{b}
Base of the triangle
\bm{h}
Height of the triangle

Examples

Example 1

Find the area of the triangle shown.

Triangle with a height of 7 centimeters and base of 10 centimeters.
Worked Solution
Create a strategy

Use the area of a triangle formula.

Apply the idea
\displaystyle A\displaystyle =\displaystyle \dfrac12\cdot b\cdot\text hUse the formula
\displaystyle =\displaystyle \dfrac12\cdot10\cdot7Substitute b=10 and h=7
\displaystyle =\displaystyle 35\text{ cm}^2Evaluate

Example 2

Alex is making a kite shaped like a triangle. He plans to use a stick that is 15\text{ cm} long for the height, and he wants the base of the kite to be 20\text{ cm}. What is the minimum amount of material Alex needs to buy?

Worked Solution
Create a strategy

We need to calculate the area of the kite.

Apply the idea
\displaystyle A\displaystyle =\displaystyle \dfrac12 b hFormula for area of a triangle
\displaystyle =\displaystyle \dfrac12\cdot20\cdot15Substitute b=20 and h=15
\displaystyle =\displaystyle 150\text{ cm}^2Evaluate the multiplication
Idea summary

The formula for the area of a triangle is:

\displaystyle A= \dfrac{1}{2} b h
\bm{A}
Area of the triangle
\bm{b}
Base of the triangle
\bm{h}
Height of the triangle

Outcomes

6.MG.2

The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles, and parallelograms.

6.MG.2a

Develop the formula for determining the area of parallelograms and triangles using pictorial representations and concrete manipulatives (e.g., two-dimensional diagrams, grid paper).

6.MG.2b

Solve problems, including those in context, involving the perimeter and area of triangles, and parallelograms.

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