Understanding how to find the area of a polygon is a necessary math skill for academic success and everyday applications. This is especially important for high school students preparing for the ACT® WorkKeys Applied Math Test.
This guide will help you calculate the area of various polygons, starting with basic shapes like rectangles and triangle. By the end, you’ll be ready to tackle polygon area questions on the ACT® WorkKeys test. Let’s get started!
What We Review
Understanding Polygons and Area
What is a Polygon?
A polygon is a flat shape that has at least three straight sides and angles. Common examples are triangles, rectangles, and pentagons. These shapes are important in geometry and are the building blocks for more complex figures. Here’s a table of common polygons and the number of sides:
| Name | Number of Sides |
| Triangle | 3 |
| Quadrilateral (including squares, rectangles, parallelograms, and trapezoids) | 4 |
| Pentagon | 5 |
| Hexagon | 6 |
| Octagon | 8 |
What Does “Area” Mean in Mathematics?
In math, the area is the size inside a flat shape. It is measured in square units, like square meters or square feet. Understanding area helps you know how big a surface is.
Basic Area Formulas for Common Polygons
Knowing how to find the area of simple shapes is important for math students. Each shape has a different formula. Learning these formulas makes it easier to solve harder problems.
Area of a Rectangle and Square
To find the area of a rectangle, you just multiply the length by the width. This works for squares too, since all sides are the same. For squares, you calculate the area by squaring one side.
Area of a Triangle
To find the area of a triangle, use the base and height with the formula: Area = 1/2 × base × height. This method applies to all triangles, making it very useful.
Area of a Parallelogram
The area of a parallelogram is calculated like that of a rectangle. You multiply the base by the height. However, in a parallelogram, the sides can be slanted.
Area of a Trapezoid
To find the area of a trapezoid, add the lengths of the two parallel sides. Multiply this sum by the height and then divide by two. This method incorporates the lengths of the non-parallel sides.
Summary of Common Areas
- Rectangle and Square: Area = length × width
- Triangle: Area = 1/2 × base × height
- Parallelogram: Area = base × height
- Trapezoid: Area = 1/2 × (base1 + base2) × height
Real-World Applications and Practice Problems
Applying Polygon Area in Real Life
Knowing how to find the area of polygons is important in areas like architecture and landscaping. It helps figure out how much material is needed and plan designs. Accurate area measurements help use resources better and plan more efficiently. To improve your skills, let’s work on area problems.
Question 1: Find the Area of a Rectangle
You are planning to create a rectangular garden in your backyard. The garden will have a length of 15 meters and a width of 10 meters. What is the area of the garden in square meters?
To find the area of the rectangular garden, use the formula:
\text{Area} = \text{length} \times \text{width}Plug in the given dimensions:
\text{Area} = 15 \text{ meters} \times 10 \text{ meters} = 150 \text{ square meters}Therefore, the area of the garden is 150 square meters.
Question 2: Find the Area of a Triangle
Next, think about a triangular garden with a base of 6 units and a height of 4 units. You can find its area with this formula:
\text{Area} = \frac{1}{2} \text{base} \times \text{height}Substituting what we know:
\text{Area} = \frac{1}{2} \times 6 \times 4This results in an area of 12 square units.
Tips for ACT® WorkKeys Applied Math Test Preparation
To prepare for the ACT® WorkKeys Applied Math Test, plan your study time effectively. Focus on understanding key concepts and practice regularly to boost your confidence in solving math problems.
Familiarize yourself with area formulas for different shapes, as this will help you tackle various test questions. Consistent practice will enhance your readiness and reduce anxiety. Remembering key formulas is essential for success. Use flashcards to memorize them, and always check your work for mistakes before moving on.
Effective time management during the test is essential. Allocate your time wisely for each question to avoid rushing. Practice answering questions with a timer to simulate test conditions and improve your pace.
Conclusion: Finding the Area of a Polygon
Knowing how to find the area of a polygon can help you in school and in everyday situations. The two most common shapes on the ACT® WorkKeys Applied Math exam are the rectangle and the triangle. Practice often with both types.
Sharpen Your Skills for ACT® WorkKeys Applied Math
Are you preparing for the ACT® WorkKeys Applied Math test? We’ve got you covered! Try our review articles designed to help you confidently tackle real-world math problems. You’ll find everything you need to succeed, from quick tips to detailed strategies. Start exploring now!
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