Mathematics
Grade 10
15 min
Area of compound figures
Area of compound figures
What you'll learn
- Identify the different shapes that make up a compound figure, such as rectangles and squares, with 80% accuracy on a worksheet.
- Solve area problems involving compound figures by breaking them down into simpler shapes and adding their areas together, achieving at least 70% correct answers on a quiz.
- Explain, using words and drawings, how to find the area of a compound figure to a partner, demonstrating understanding of the process.
- Apply the formula for area (length x width) correctly to calculate the area of rectangles and squares within compound figures in 4 out of 5 examples.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Decompose a compound figure on the coordinate plane into simpler polygons like triangles and rectangles.
Calculate the lengths of horizontal, vertical, and diagonal sides of a polygon using coordinate differences and the distance formula.
Calculate the area of a compound figure using the addition (decomposition) method.
Calculate the area of a compound figure using the subtraction (bounding box) method.
Apply the Shoelace Formula to find the area of any simple polygon given its vertices.
Solve multi-step problems involving the area of composite shapes in a coordinate system.
Ever wondered how a video game designer calculates the exact area of a complex kingdom on a map, or how an architect finds the square footage of an L-shaped room? 🗺️ Let's find o...
2
Key Concepts & Vocabulary
TermDefinitionExample
Compound FigureA geometric figure that is formed by combining two or more simpler geometric shapes, such as rectangles, triangles, or trapezoids.An L-shaped polygon can be seen as two rectangles joined together, or one large rectangle with a smaller rectangle removed from a corner.
VerticesThe corner points of a polygon. On the coordinate plane, each vertex is defined by an ordered pair (x, y).A triangle has three vertices, such as A(1, 2), B(5, 2), and C(3, 6).
Decomposition MethodA strategy to find the area of a compound figure by breaking it down into smaller, non-overlapping, simple shapes. The total area is the sum of the areas of these smaller shapes.Splitting a plus-shaped figure into five squares and adding their individual areas together.
Subtraction Method...
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Core Formulas
Distance Formula
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Use this to find the length of any side of a polygon, especially diagonal ones, given the coordinates of its endpoints (x1, y1) and (x2, y2). This is essential for finding the base or height of triangles in the decomposition method.
Area Formulas for Simple Shapes
Rectangle: A = l \times w
Triangle: A = \frac{1}{2} b \times h
These are the building blocks for the Decomposition and Subtraction methods. After breaking down a compound figure, you apply these fundamental formulas to each simple shape.
Shoelace Formula
A = \frac{1}{2} |(x_1y_2 + x_2y_3 + ... + x_ny_1) - (y_1x_2 + y_2x_3 + ... + y_nx_1)|
The most direct method for finding the area of a polygon with 'n' vertices. List the vertices (x, y) i...
5 more steps in this tutorial
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Challenging
When using the Shoelace Formula, if three consecutive vertices of a polygon, say A, B, and C, are collinear (lie on the same straight line), what is the relationship between the area calculated for polygon ABCD... and the area of polygon ACD...?
A.The area will be zero.
B.The areas will be identical.
C.The area of ABCD... will be larger.
D.The area of ABCD... will be smaller.
Challenging
A quadrilateral has vertices A(0,5), B(-4,2), C(0,-1), and D(x,2). If the area of the quadrilateral is 24 square units and x > 0, what is the value of x?
A.2
B.3
C.5
D.4
Challenging
A large triangle is defined by vertices P(0,0), Q(10,4), and R(2,8). A smaller, compound figure is formed by connecting the midpoints of sides PQ, QR, and RP. What is the area of this smaller figure (a triangle)?
A.9 square units
B.36 square units
C.18 square units
D.12 square units
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Frequently asked questions
What grade level is "Area of compound figures"?
Area of compound figures is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Area of compound figures?
You'll be able to: Identify the different shapes that make up a compound figure, such as rectangles and squares, with 80% accuracy on a worksheet; Solve area problems involving compound figures by breaking them down into simpler shapes and adding….
Is "Area of compound figures" 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 of compound figures?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.