Pre-Algebra
Geometry
Area of triangles, quadrilaterals and polygons
20 practice questions
0 video lessons
Theory + worked examples
Area of Triangles, Quadrilaterals and Polygons
California Pre-Algebra • Standard 6.G.1 • Geometry
Area of Triangles, Quadrilaterals and Polygons is the opening topic of Geometry in the California Common Core State Standards. It is aligned to Standard 6.G.1, which requires students to find the area of triangles, quadrilaterals, and polygons.
Area measures the space inside a shape; each polygon has a formula built from base and height.
Theory
Area is the number of unit squares that fit inside a shape.
- Triangle: \(\dfrac{1}{2}bh\).
- Rectangle: \(lw\); parallelogram: \(bh\).
- Trapezoid: \(\dfrac{1}{2}(b_1+b_2)h\).
Height is perpendicular to the base.
Base and height of a triangle.
Area formulas.
Key areas:
\[A_{\triangle}=\dfrac{1}{2}bh,\quad A_{\square}=lw,\quad A_{\text{trap}}=\dfrac{1}{2}(b_1+b_2)h\]
Area is in square units.
How to find area
- Identify the shape.
- Find the base and perpendicular height.
- Apply the matching formula.
- Label the answer in square units.
Example 1 — Triangle
Find the area of a triangle with base \(10\) and height \(6\).
Solution
Half base times height.
| \(\dfrac{1}{2}(10)(6)\) | \(=\) | \(30\) |
Example 2 — Rectangle
Find the area of a \(8\times5\) rectangle.
Solution
Length times width.
| \(8\cdot5\) | \(=\) | \(40\) |
Example 3 — Parallelogram
Find the area with base \(7\) and height \(4\).
Solution
Base times height.
| \(7\cdot4\) | \(=\) | \(28\) |
Example 4 — Trapezoid
Bases \(6\) and \(10\), height \(4\). Find the area.
Solution
Average the bases, times height.
| \(\dfrac{1}{2}(6+10)(4)\) | \(=\) | \(32\) |
Common pitfalls
Use the perpendicular height, not a slanted side.
Don't forget the \(\dfrac12\) for triangles.
Area is squared units.
Frequently asked questions
What is area?
The space inside a shape, in square units.
What is a triangle's area?
\(\dfrac12\) base times height.
What height do I use?
The perpendicular height.
Area of a \(10\times6\) triangle?
\(30\).
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