Mathematics
Grade 10
15 min
Area and perimeter in the coordinate plane: Set 1
Area and perimeter in the coordinate plane: Set 1
What you'll learn
- Identify the percentage, the whole, and the part in word problems with 80% accuracy.
- Solve for the percent of a number using visual models (e.g., bar models, grids) in at least 3 out of 4 attempts.
- Calculate the percent of a number using multiplication with 75% accuracy on a worksheet containing 12 problems.
- Explain in writing, using at least two sentences, how to find 25% of a number.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the perimeter of a polygon given its vertices in the coordinate plane by applying the Distance Formula.
Determine the area of triangles and rectangles with horizontal or vertical sides.
Apply the 'boxing in' (enclosure) method to find the area of any polygon.
Decompose a complex polygon into simpler shapes (rectangles and triangles) to find its total area.
Use the Shoelace Formula as an efficient method for calculating the area of a simple polygon.
Verify the properties of a polygon (e.g., right angles) using slope to simplify area calculations.
Ever wondered how a GPS calculates the area of a park or a property lot just from a few coordinates? 🗺️ Let's learn the geometry behind it!
This tutorial reviews how to use coordinate geo...
2
Key Concepts & Vocabulary
TermDefinitionExample
Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal line called the x-axis and a vertical line called the y-axis. Points are located using ordered pairs (x, y).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. In the coordinate plane, each vertex is represented by an ordered pair.A triangle could have vertices at A(0, 0), B(5, 0), and C(2, 3).
PerimeterThe total distance around the exterior of a polygon. It is calculated by summing the lengths of all its sides.For a triangle with side lengths 3, 4, and 5, the perimeter is 3 + 4 + 5 = 12 units.
AreaThe measure of the two-dimensional space enclosed within a polygon, measured in square units.A rectangle with a length...
3
Core Formulas
Distance Formula
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Use this formula to calculate the length of a line segment (the distance) between any two points (x₁, y₁) and (x₂, y₂). This is essential for finding the side lengths of a polygon to calculate its perimeter.
Slope Formula
m = \frac{y_2 - y_1}{x_2 - x_1}
Use this formula to find the slope of a line segment. Slopes can be used to determine if sides are parallel (equal slopes) or perpendicular (slopes are negative reciprocals, e.g., 2/3 and -3/2), which helps identify shapes like rectangles and right triangles.
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 simple polygon given its vertices (x₁, y₁), (x₂, y₂), ..., (...
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Challenging
A rectangle has vertices at A(1, 2), B(5, 2), and C(5, 7). What are the coordinates of the fourth vertex, D, and what is the area of the rectangle?
A.D(1, 5); Area = 15 square units
B.D(2, 7); Area = 20 square units
C.D(1, 7); Area = 20 square units
D.D(1, 7); Area = 18 square units
Challenging
A triangle has vertices at A(0, 0), B(8, 0), and C(k, 5). If the area of the triangle is 20 square units, what is a possible value of k?
A.5
B.4
C.8
D.2.5
Easy
In the context of the coordinate plane, what are the 'vertices' of a polygon?
A.The lengths of the sides of the polygon.
B.The total distance around the polygon.
C.The corner points of the polygon, represented by ordered pairs.
D.The space enclosed by the polygon.
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What grade level is "Area and perimeter in the coordinate plane: Set 1"?
Area and perimeter in the coordinate plane: Set 1 is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Area and perimeter in the coordinate plane: Set 1?
You'll be able to: Identify the percentage, the whole, and the part in word problems with 80% accuracy; Solve for the percent of a number using visual models (e.g., bar models, grids) in at least 3 out of 4 attempts; Calculate the percent of a….
Is "Area and perimeter in the coordinate plane: Set 1" free to practice?
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How many practice questions are included with Area and perimeter in the coordinate plane: Set 1?
This lesson includes 41 practice questions across multiple difficulty levels, each with instant feedback and explanations.