Mathematics
Grade 10
15 min
Area and perimeter of figures on grids
Area and perimeter of figures on grids
What you'll learn
- Identify the area and perimeter of rectangles and squares drawn on a grid by counting the units and unit lengths.
- Calculate the area of irregular figures on a grid by composing and decomposing them into rectangles and squares, and then adding the individual areas, with at least 80% accuracy.
- Determine the perimeter of irregular figures on a grid by counting the unit lengths along the outer edges, achieving at least 80% accuracy.
- Explain, using drawings and words, how to find the area and perimeter of a figure on a grid to a partner.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the perimeter of a polygon on a coordinate grid by finding the length of each side.
Apply the Distance Formula to find the lengths of diagonal sides of a polygon.
Calculate the area of polygons using the decomposition method (the 'box method').
Apply the Shoelace Formula to efficiently find the area of any polygon given its vertices.
Differentiate between perimeter (a measure of length) and area (a measure of space) in coordinate geometry problems.
Verify the properties of a geometric figure (e.g., parallelogram, rectangle) using coordinate formulas before calculating its area.
Ever wondered how a GPS calculates the area of a park or a property lot just from its corner coordinates? 🗺️ Let's unlock the geometric secrets behind the...
2
Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal x-axis and a vertical y-axis. It's the grid on which we plot our figures.The point P(4, -2) is located 4 units to the right of the origin and 2 units down.
VerticesThe corner points of a polygon. On a grid, each vertex is represented by an ordered pair (x, y).A triangle might have vertices at A(1, 5), B(3, 1), and C(-2, 1).
PerimeterThe total distance around the outside of a polygon. It is a measure of length, found by adding the lengths of all its sides.For a rectangle with vertices at (0,0), (5,0), (5,3), and (0,3), the side lengths are 5, 3, 5, and 3. The perimeter is 5 + 3 + 5 + 3 = 16 units.
AreaThe measure of the two-dimensional space enclosed by a polygon, expressed in squa...
3
Core Formulas
The Distance Formula
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Use this to find the exact length of any side of a polygon that is not perfectly horizontal or vertical. It applies the Pythagorean theorem to the coordinates of the two endpoints, (x₁, y₁) and (x₂, y₂).
The Shoelace Formula
A = \frac{1}{2} |(x_1y_2 + x_2y_3 + ... + x_ny_1) - (y_1x_2 + y_2x_3 + ... + y_nx_1)|
A powerful method to find the area of any polygon when you know the coordinates of its vertices. List the vertices in counter-clockwise order, repeating the first vertex at the end, then perform the cross-multiplication as shown.
5 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
Which of the following best defines the perimeter of a polygon on a coordinate grid?
A.The number of square units inside the polygon.
B.The length of the longest side of the polygon.
C.The total length of the boundary of the polygon.
D.The space enclosed by the polygon's vertices.
Easy
To find the length of a diagonal side of a polygon connecting vertices (x₁, y₁) and (x₂, y₂), which formula should be used?
A.d = √((x₂ - x₁)² + (y₂ - y₁)²)
B.= (1/2) * base * height
C.m = (y₂ - y₁) / (x₂ - x₁)
D.= (1/2) |(x₁y₂ + ...) - (y₁x₂ + ...)|
Easy
What is the length of the horizontal segment connecting the vertices A(2, 5) and B(9, 5)?
A.5 units
B.7 units
C.4 units
D.11 units
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Frequently asked questions
What grade level is "Area and perimeter of figures on grids"?
Area and perimeter of figures on grids is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Area and perimeter of figures on grids?
You'll be able to: Identify the area and perimeter of rectangles and squares drawn on a grid by counting the units and unit lengths; Calculate the area of irregular figures on a grid by composing and decomposing them into rectangles and squares….
Is "Area and perimeter of figures on grids" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Area and perimeter of figures on grids?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.